Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Bibliography
Ahlberg, R. and Lindner, P., The Fermi correlation for electrons in momentum space, J Phys B, Vol 9(17), p 2963–9, 1976.
Ahlenius, Tor and Lindner, Peter., Semiempirical MO wave functions in momentum space, J Phys B, Vol 8(5), p 778–95, 1975.
Akhiezer, A.I. and Berestetskii, V.B., Quantum Electrodynamics, Interscience, New York, 1965.
Allan, Neil L. and Cooper, David L., Local density approximations and momentum-space properties in light molecules and ionic solids, J Chem Soc, Faraday Trans 2, Vol 83(9), p 1675–87, 1987.
Allan, Neil L. and Cooper, David L., Momentum space properties and local density approximations in small molecules: a critical appraisal, J Chem Phys, Vol 84(10), p 5594–605, 1986.
Alliluev, S.P., Sov Phys JETP, Vol 6, p 156, 1958.
Amiet, J.-P. et Huguenin, P., Mécaniques classique et quantiques dans l’espace de phase, Universitéde Neuchâtel, 1981.
Amos, A.T. and Hall, G.G., Proc. Roy. Soc. London, Vol A263, p 483, 1961.
Anderson, R.W.; Aquilanti, V.; Cavalli, S. and Grossi, G., J Phys Chem, Vol 95, p 8184, 1991.
Anderson, R.W.; Aquilanti, V.; Cavalli, S. and Grossi, G., J Phys Chem, Vol 97, p 2443, 1993.
Aquilanti, V. and Cavalli, S., Coordinates for molecular dynamics, J Chem Phys, Vol 85, p 1355–1361, 1986.
Aquilanti, V., Cavalli, S., De Fazio, D, and Grossi, G. Hyperangular Momentum: Applications to Atomic and Molecular Science, in New Methods in Quantum Theory, Tsipis, C.A., Popov, V.S., Herschbach, D.R., and Avery, J.S., Eds., Kluwer, Dordrecht, 1996.
Aquilanti, V.; Cavalli, S. and Grossi, G., Hyperspherical coordinates for molecular dynamics by the method of trees and the map ping of potential-energy surfaces for triatomic systems, J Chem Phys, Vol 85, p 1362, 1986.
Aquilanti, V.; Grossi, G.; Laganá, A.; Pelikan, E., and Klar, H., A decoupling scheme for a 3-body problem treated by expansionns into hyperspherical harmonics. The hydrogen molecular ion, Lett Nuovo Cimento, Vol 41, 541, 1984.
Aquilanti, V.; Grossi, G., and Laganá, A., On hyperspherical mapping and harmonic expansions for potential energy surfaces J Chem Phys, Vol 76, p 1587–1588, 1982.
Aquilanti, V.; Laganá, A., and Levine, R.D., Chem Phys Lett, Vol 158, p 87, 1989.
Aquilanti, V. and Cavalli, S., Chem Phys Lett, Vol 141, p 309, 1987.
Aquilanti, V.; Cavalli, S.; Grossi, G.; Rosi, M.; Pellizzari, V.; Sgamellotti, A., and Tarantelli, F.; Chem Phys Lett, Vol 16, p 179, 1989.
Aquilanti, V.; Cavalli, S.; Grossi, G., and Anderson, R.W., J Chem Soc Faraday Trans, Vol 86, p 1681, 1990.
Aquilanti, V.; Benevente, L.; Grossi, G. and Vecchiocattivi, F., Coupling schemes for atom-diatom interactions, and an adiabatic decoupling treatment of rotational temperature effects on glory scattering, J Chem Phys, Vol 89, 751–761, 1988.
Aquilanti, V. and Grossi, G., Angular momentum coupling schemes in the quantum mechanical treatment of P-state atom collisions J Chem Phys, Vol 73, p 1165–1172, 1980.
Aquilanti, V.; Cavalli, S., and Grossi, G., Theor Chem Acta, Vol 79, p 283, 1991.
Aquilanti, V. and Cavalli, S., Few Body Systems, Suppl 6, p 573, 1992.
Aquilanti, V. and Grossi, G., Lett Nuovo Cimento, Vol 42, p 157, 1985.
Aquilanti, V. Cavalli, S. and De Fazio, D., Angular and hyperangular momentum coupling coefficients as Hahn polynomials, J Phys Chem Vol 99, p 15694, 1995.
Aquilanti, V., Cavalli, S., Coletti, C. and Grossi, G., Alternative Sturmian bases and momentum space orbitals; an application to the hydrogen molecular ion, Chem Phys Vol 209, p 405, 1996.
Aquilanti, V., Cavalli, S. and Coletti, C., The d-dimensional hydrogen atom; hyperspherical harmonics as momentum space orbitals and alternative Sturmian basis sets, Chem Phys Vol 214, p 1, 1997.
Aquilanti, V., and Avery, J., Generalized Potential Harmonics and Contracted Sturmians, Chem. Phys. Letters, Vol 267, p 1, 1997.
Avery, John and Ørmen, Per-Johan, Int. J. Quantum Chem. Vol 18, p 953, 1980.
Avery, John, Hyperspherical Harmonics; Applications in Quantum Theory, Kluwer Academic Publishers, Dordrecht, 1989.
Avery, John, Hyperspherical Sturmian Basis Functions an Reciprocal Space, in New Methods in Quantum Theory, Tsipis, C.A., Popov, V.S., Herschbach, D.R., and Avery, J.S., Eds., Kluwer, Dordrecht, 1996.
Avery, John and Antonsen, Frank, A new approach to the quantum mechanics of atoms and small molecules, Int J Quantum Chem, Symposium 23, p 159, 1989.
Avery, John and Antonsen, Frank, Iteration of the Schrödinger equation, starting with Hartree-Fock wave functions, Int J Quantum Chem, Vol 42, p 87, 1992.
Avery, John and Antonsen, Frank, Theor. Chim. Acta, Vol 85, p 33, 1993.
Avery, John and Herschbach, Dudley R., Hyperspherical sturmian basis functions, Int J Quantum Chem, Vol 41, p 673, 1992.
Avery, John and Wen, Zhen-Yi, A Formulation of the quantum mechanical many-body in terms of hyperspherical coordinates, Int J Quantum Chem Vol 25, p 1069, 1984.
Avery, John, Correlation in iterated solutions of the momentum-space Schrödinger equation, Chem Phys Lett, Vol 138(6), p 520–4, 1987.
Avery, John, Hyperspherical Harmonics; Some Properties and Applications, in Conceptual Trends in Quantum Chemistry, Kryachko, E.S., and Calais, J.L., Eds, Kluwer, Dordrecht, 1994.
Avery, John, Hansen, T.B., Wang, M. and Antonsen, F., Sturmian basis sets in momentum space, Int J Quant Chem Vol 57, p 401, 1996.
Avery, John, and Hansen, Tom Børsen, A momentum-space picture of the chemical bond Int J Quant Chem Vol 60, p 201, 1996.
Avery, John, Many-Particle Sturmians, J Math Chem, Vol 21, p 285, 1997.
Avery, John and Antonsen, Frank, Relativistic Sturmian Basis Functions, J. Math. Chem. Vol 24, p 175, 1998.
Avery, John, A Formula for Angular and Hyperangular Integration, J. Math. Chem., Vol 24, p 169, 1998.
Avery, John, Many-electron Sturmians applied to atoms and ions, J. Mol. Struct. Vol 458, p 1, 1999.
Avery, John, Many-Electron Sturmians as an Alternative to the SCF-CI Method, Adv. Quantum Chem., Vol. 31, p 201, 1999.
Ballot, L. and Farbre de la Ripelle, M., Application of the hyperspherical formalism to trinucleon bound-state problems, Ann Phys, Vol. 127, p 62, 1980.
Bandar, M. and Itzyksen, C., Group theory and the H atom, Rev Mod Phys Vol 38, p 330, p 346, 1966.
Bang, J.M. and Vaagen, J.S., The Sturmian expansion: a well-depth-method for orbitals in a deformed potential, Z Phys A, Vol 297(3), p 223–36, 1980.
Bang, J.M., Gareev, F.G., Pinkston, W.T. and Vaagen, J.S., Phys Rep Vol 125, p 253–399, 1985.
Bar-yudin, L.E. and Tel-nov, D. A., Sturmian expansion of the electron density deformation for 3d-metal ions in electric field, Vestn Leningr Univ, Ser 4: Fiz, Khim (1), p 83–6, 1991.
Baretty, Reinaldo; Ishikawa, Yasuyuki; and Nieves, Jose F., Momentum space approach to relativistic atomic structure calculations, Int J Quantum Chem, Quantum Chem Symp, Vol 20, p 109–17, 1986.
Benesch, Robert and Smith, Vedene H. Jr., Natural orbitals in momentum space and correlated radial momentum distributions. I. The 1S ground state of Li+, Int J Quantum Chem, Symp, Vol No. 4, p 131–8, 1971.
Biedenharn, L.C. and Louck, J.D., Angular Momentum in Quantum Physics, Addison Wesley, Reading, Mass, 1981.
Biedenharn, L.C. and Louck, J.D., The Racah-Wigner Algebra in Quantum Theory, Addison Wesley, Reading, Mass, 1981.
Blinder, S.M., On Green’s functions, propagators, and Sturmians for the nonrelativistic Coulomb problem, Int J Quantum Chem, Quantum Chem Symp, Vol 18, p 293–307, 1984.
Bransden, B.H.; Noble, C.J.; and Hewitt, R.N., On the reduction of momentum space scattering equations to Fredholm form, J Phys B: At, Mol Opt Phys, Vol 26(16), p 2487–99, 1993.
Brion, C.E., Looking at orbitals in the laboratory: the experimental investigation of molecular wave functions and binding energies by electron momentum spectroscopy, Int J Quantum Chem, Vol 29(5), p 1397–428, 1986.
Brink, D.M. and Satchler, G.R., Angular Momentum, Oxford University Press, 1968.
Calais, J-L.; Defranceschi, M.; Fripiat, J.G. and Delhalle, J., Momentum space functions for polymers, J Phys: Condens Matter, Vol 4(26), p 5675–91, 1992.
Calais, Jean-Louis, Fukutome classes in momentum space, Theor Chim Acta, Vol 86(1–2), p 137–47, 1993.
Calais, Jean-Louis, Orthogonalizationin momentum space, Int J Quantum Chem, Vol 35(6), p 735–43, 1989.
Calais, Jean-Louis, Pathology of the Hartree-Fock method in configuration and momentum space, J Chim Phys Phys-Chim Biol, Vol 84(5), p 601–6, 1987.
Chen, Joseph Cheng Yih and Ishihara, Takeshi, Hydrogenic-and Sturrnian-function expansions in three-body atomic problems, Phys Rev, Vol 186(1), p 25–38, 1969.
Chiu, T.W., Non-relativistic bound-state problems in momentum space, J Phys A: Math Gen, Vol 19(13), p 2537–47, 1986.
Cinal, Marek, Energy functionals in momentum space: exchange energy, quantum corrections, and the Kohn-Sham scheme, Phys Rev A, Vol 48(3), p 1893–902, 1993.
Clark, Charles W. and Taylor, K.T., The quadratic Zeeman effect in hydrogen Rydberg series: application of Sturmian functions, J Phys B, Vol 15(8), p 1175–93, 1982.
Clementi, E., J. Chem. Phys. Vol 38, p 996, 1963.
Cohen, L., Generalized phase-space distribution functions, J Math Phys, Vol 7, 781–786, 1966.
Cohen, Leon and Lee, Chongmoon, Correlation hole and physical properties: a model calculation, Int J Quantum Chem, Vol 29(3), p 407–24, 1986.
Coletti, Cecilia, Struttura Atomica e Moleculare Come Rottura, della Simmetria Ipersferica, Ph.D. thesis, Chemistry Department, University of Perugia, Italy, 1998.
Collins, L.A. and Merts, A.L., Atoms in strong, oscillating electric fields: momentum-space solutions of the time-dependent, three dimensional Schrödinger equation, J Opt Soc Am B: Opt Phys, Vol 7(4), p 647–58, 1990.
Coulson, C.A., Momentum distribution in molecular systems. I. Single bond. III. Bonds of higher order, Proc Camb Phys Soc, Vol 37, p 55, p 74, 1941.
Coulson, C.A. and Duncanson, W.E., Momentum distribution in molecular systems. II. C and C-H bond, Proc Camb Phys Soc, Vol 37, p 67, 1941.
Dahl, Jens Peder, The Wigner function, Physica A, Vol 114, p 439, 1982.
Dahl, Jens Peder, On the group of translations and inversions of phase space and the Wigner function, Phys Scripta, Vol 25, 499–503, 1982.
Dahl, Jens Peder, Dynamical equations for the Wigner functions, in Energy Storage and Redistribution in Molecules, p 557–571, Ed. J. Hinze, Plenum, New York, 1983.
Dahl, Jens Peder, The phase-space representation of quantum mechanics and the Bohr-Heisenberg correspondence principle, in Semiclassical Description of Atomic and Nuclear Collisions, p 379–394, Eds. Bang, J. and De Boer, J., North Holland, Amsterdam, 1985.
Dahl, Jens Peder, The dual nature of phase-space representations, in Classical and Quantum Systems, p 420–423, Eds: Doebner, H.D. and Schroeck, F., Jr., World Scientific, Singapore, 1993.
Dahl, Jens Peder, A phase space essay, in Conceptual Trends in Quantum Chemistry, p 199–224, Eds: Kryachko, E.S. and Calais, J.L., Kluwer Academic Publishers, Dordrecht, Netherlands, 1994.
Dahl, Jens Peder and Springborg, Michael, The Morse oscillator in position space, momentum space, and phase space J Chem Phys, Vol 88(7), p 4535–47, 1988.
Dahl, Jens Peder and Springborg, Michael, Wigner’s phase-space function and atomic structure. I. The hydrogen atom, J Mol Phys, Vol 47, p 1001, 1982.
Das, G.P.; Ghosh, S.K.; and Sahni, V.C., On the correlation energy density functional in momentum space, Solid State Commun, Vol 65(7), p 719–21, 1988.
Davies, R.W. and Davies, K.T.R., On the Wigner distribution function for an oscillator, Ann Physics, Vol 89, p 261–273, 1975.
De-Prunele, E. O(4,2) coherent states and hydrogenic atoms, Phys Rev A, Vol 42(5), p 2542–9, 1990.
De-Windt, Laurent; Defranceschi, Mireille; and Delhalle, Joseph, Variation-iteration method in momentum space: determination of Hartree-Fock atomic orbitals, Int J Quantum Chem, Vol 45(6), p 609–18, 1993.
Defranceschi, M.; Suard, M. and Berthier, G., Numerical solution of Hartree-Fock equations for a polyatomic molecule: linear triatomic hydrogen in momentum space, Int J Quantum Chem, Vol 25(5), p 863–7, 1984.
Defranceschi, M.; Suard, M.; and Berthier, G., Epitome of theoretical chemistry in momentum space, Folia Chim Theor Lat, Vol 18(2), p 65–82, 1990.
Defranceschi, M., Theoretical investigations of the momentum densities for molecular hydrogen, Chem Phys, Vol 115(3), p 349–58, 1987.
Defranceschi, Mireille and Delhalle-Joseph., Numerical solution of the Hartree-Fock equations for quasi-one-dimensional systems: prototypical calculations on the (hydrogen atom) x chain, Phys Rev B: Condens Matter, Vol 34 (8, Pt. 2), p 5862–73, 1986.
Defranceschi, Mireille and Delhalle-Joseph, Momentum space calculations on the helium atom, Eur J Phys, Vol 11(3), p 172–8, 1990.
Delande, D. and Gay, J.C., The hydrogen atom in a magnetic field. Spectrum from the Coulomb dynamical group approach, J Phys B: At Mol Phys, Vol 19(6), p L173–L178, 1986.
Delhalle, Joseph and Defranceschi and Mireille, Toward fully numerical evaluation of momentum space Hartree-Fock wave functions. Numerical experiments on the helium atom, Int J Quantum Chem, Quantum Chem Symp, Vol 21, p 425–33, 1987.
Delhalle, Joseph; Fripiat, Joseph G.; and Defranceschi, Mireille, Improving the one-electron, states of ab initio GTO calculations in momentum space. Tests on two-electron systems: hydride, helium, and lithium,(1+), Bull Soc Chim Bclg, Vol 99(3), p 135–45, 1990.
Delhalle, Joseph and Harris, Frank E., Fourier-representation method for electronic structure of chainlike systems: restricted Hartree-Fock equations and applications to the atomic hydrogen (H)x chain in a basis of Gaussian, functions, Phys Rev B: Condens Matter, Vol 31(10), p 6755–65, 1985.
Deloff, A. and Law, J., Sturmian expansion, method for bound state problems, Phys Rev C, Vol 21(5), p 2048–53, 1980.
Denteneer, P.J.H. and Van Haeringen, W., The pseudopotential-density-functional method in momentum space: details and test cases, J Phys C, Vol 18(21), p 4127–42, 1985.
Desclaux, J.P., Comput. Phys. Commun., Vol 9, p 31, 1975.
Desclaux, J.P., Phys. Schripa, Vol 21, p 436, 1980.
Dirac, P.A.M., Note on exchange phenomena in the Thomas atom, Proc Camb Phil Soc, Vol 26, 376–385, 1930.
Dorr, Martin; Potvliege, R.M.; and Shakeshaft, Robin, Atomic hydrogen irradiated by a strong laser field: Sturmian basis calculations of rates for high-order multiphoton ionization, Raman scattering, and harmonic generation, J Opt Soc Am B: Opt Phys, Vol 7(4), p 433–48, 1990.
Douglas, Marvin., Coulomb perturbation calculations in momentum space and application to quantum-electrodynamic hyperfine-structure corrections, Phys Rev A, Vol 11(5), p 1527–38, 1975.
Drake, G.W.F. and Goldman, S.P., Relativistic Sturmian and finite basis set methods an atomic physics, Adv At Mol Phys, Vol 25, p 393–416, 1988.
Dube, L.J. and Broad, J.T., Sturmian discretization. II. The off-shelf Coulomb wavefunction, J Phys B: At, Mol Opt Phys, Vol 23(11), p 1711–32, 1990.
Dube, Louis J. and Broad, John T., Sturmian discretization: the off-shell Coulomb wave function, J Phys B: At, Mol Opt Phys, Vol 22(18), p L503, 1989.
Duchon, C; Dumont-Lepage, M.C.; and Gazeau, J.P., On two Sturmian alternatives to the LCAO method for a many-center one-electron system, J Chem Phys, Vol 76(1), p 445–7, 1982.
Duchon, C.; Dumont-Lepage, M.C.; and Gazeau, J.P., Sturmian methods for the many-fixed-centers Coulomb potential, J Phys A: Math Gen, Vol 15(4), p 1227–41, 1982.
Duffy, Patrick; Casida, Mark E; Brion, C.E; and Chong, D.P., Assessment of Gaussian-weighted angular resolution functions in the comparison of quantum-mechanically calculated electron momentum distributions with experiment Chem Phys, Vol 159(3), p 347–63, 1992.
Duncanson, W.E., Momentum distribution in molecular systems. IV. H molecule ion, H +2 , Proc Camb Phil Soc, Vol 37, p 47, 1941.
Dunlap, B.I., Chem Phys Lett, Vol 30, p 39, 1975.
Edmonds, A.R., Angular Momentum in Quantum Chemistry, Princeton University Press, 1960.
Edmonds, A.R., Quadratic Zeeman effect. I. Application of the sturmian functions, J Phys B, Vol 6(8), p 1603–15, 1973.
Englefield, M.J., Group theory and the Coulomb problem, Wiley-Interscience, New York, 1972.
Epstein, P.S., Proc. Natl. Acad. Sci. (USA), Vol 12, p 637, 1926.
Eyre, D. and Miller, H.G., Sturmian projection and an L2 discretization of three-body continuum effects, Phys Rev c: Nucl Phys, Vol 32(3), p 727–37, 1985.
Eyre, D. and Miller, H.G., Sturmian approximation of three-body continuum effects, Phys Lett B, Vol 153B(1–2), p 5–7, 1985.
Eyre, D. and Miller, H.G., Sturmian expansion approximation to three-body scattering, Phys Lett B, Vol 129B(1–2), p 15–17, 1983.
Fano, Ugo, Wave propagation and diffraction on a potential ridge, Phys Rev Vol A 22, p 2660, 1980.
Fano, Ugo, Unified treatment of collisions, Phys Rev Vol A 24, p 2402, 1981.
Fano, Ugo, Correlations of two excited electrons, Rep Prog Phys Vol 46, p 97, 1983.
Fano, Ugo and Rao, A.R.P., Atomic Collisions and Spectra, Academic Press, Orlando, Florida, 1986.
Fernández Rico, J., Ramírez, G., López, R., and Fernández Alonso, J.I., Collect,. Czech. Chem. Comm., Vol 53, p 2250, 1987.
Fernández Rico, J., López, R., Ema, I., and Ramírez, G., preprints, 1997.
Flores, J.C., Kicked quantum rotator with dynamic disorder: a diffusive behavior in momentum space, Phys Rev A, Vol 44(6), p 3492–5, 1991.
Fock, V.A., Z. Phys., Vol 98, p 145, 1935.
Fock, V.A., Hydrogen atoms and non-Euclidian geometry, Kgl Norske Videnskab Forh, Vol 31, p 138, 1958.
Fonseca, A.C. and Pena, M.T., Rotational-invariant Sturmian-Faddeev ansatx for the solution of hydrogen molecular ion (H2+): a general approach to molecular three-body problems, Phys Rev A: Gen Phys, Vol 38(10), p 4967–84, 1988.
Fonseca, A.C., Four-body equations in momentum space, Lect Notes Phys, Vol 273 (Models Methods Few-Body Phys.), p 161–200, 1987.
Fripiat, J.G.; Delhalle, J. and Defranceschi, M., A momentum space approach to improve ab initio Hartree-Fock results based on the LCAO-GTF approximation, NATO ASI Ser, Ser C, Vol 271 (Numer. Determ. Electron. Struct. At., Diat. Polyat. Mol.), p 263–8, 1989.
Gadre, Shridhar R. and Bendale, Rajeev D., Maximization of atomic information-entropy sum in configuration and momentum spaces, Int J Quantum Chem, Vol 28(2), p 311–14, 1985.
Gadre, Shridhar R. and Chakravorty, Subhas, The self-interaction correction to the local spin density model: effect on atomic momentum space properties, Chem Phys Lett, Vol 120(1), p 101–5, 1985.
Gallaher, D.F. and Wilets, L., Coupled-state calculations of proton-hydrogen scattering in the Sturmian representation, Phys Rev, Vol 169(1), p 139–49, 1968.
Gazeau, J.P. and Maquet, A., A new approach to the two-particle Schrödinger bound state problem, J Chern Phys, Vol 73(10), p 5147–54, 1980.
Gazeau, J.P. and Maquet, A., Bound states in a Yukawa potential: a Sturmian group theoretical approach, Phys Rev A, Vol 20(3), p 727–39, 1979.
Geller, M., Two-center Coulomb integrals, J Chem Phys, Vol 41, p 4006, 1964.
Gerry, Christopher C., Inner-shell bound-bound transitions from variationally scaled Sturmian functions, Phys Rev A: Gen Phys, Vol 38(7), p 3764–5, 1988.
Ghosh, Swapan K., Quantum chemistry in phase space: some current trends, Proc-Indian Acad Sci, Chem Sci, Vol 99(1–2), p 21–8, 1987.
Gloeckle W., Few-body equations and their solutions in momentum space, Lect Notes Phys, Vol 273 (Models Methods Few-Body Phys.), p 3–52, 1987.
Goscinski, O., Preliminary Research Report No. 217, Quantum Chemistry Group, Uppsala University, 1968.
Gradshteyn, I.S. and Ryshik, I.M., Tables of Integrals, Series and Products, Academic Press, New York, (1965).
Grant, I.P., in Relativistic Effects in Atoms and Molecules, Wilson, S., Ed., Plenum Press, 1988.
Grant, I.P., in Atomic, Molecular and Optical Physics Handbook, Drake, G.W.F. Ed., Chapt 22, p 287, AIP Press, Woodbury New York, 1996.
Gruzdev, P.F.; Soloveva, G.S. and Sherstyuk, A.I., Calculation of neon and argon steady-state polarizabilities by the method of Hartree-Fock SCF Sturmian expansion, Opt Spektrosk, Vol 63(6), p 1394–7, 1987.
Haftel, M.I. and Mandelzweig, V.B., A fast convergent hyper-spherical expansion for the helium ground state, Phys Letters, Vol A 120, p 232, 1987.
Han, C.S., Electron-atom scattering in an intense radiation field, Phys Rev A: At, Mol, Opt Phys, Vol 51(6), p 4818–23, 1995.
Hansen, T.B., The many-center one-electron problem in momentum space, Thesis, Chemical Institute, University of Copenhagen, 1998.
Harris, F.E. and Michels, H.H., Adv. Chem. Phys. 13, 205, 1967.
Hartt, K. and Yidana, P.V.A., Analytic Sturmian functions and convergence of separable expansions, Phys Rev C: Nucl Phys, Vol 36(2), p 475–84, 1987.
Heddle, David P; Kwon, Yong Rae and Tabakin, F., Coulomb plus strong interaction bound states-momentum space numerical solutions, Comput Phys Commun, Vol 38(1), p 71–82, 1985.
Heller, E.J., Wigner phase space method: Analysis for semiclassical applications, J Chem Phys, Vol 65, 1289–1298, 1976.
Henderson, George A., Variational theorems for the single-particle probability density and density matrix in momentum space, Phys Rev A, Vol 23(1), p 19–20, 1981.
Henriksen, N.E., Billing, G.D. and Hansen, F.Y., Phase-space representation of quantum mechanics: Dynamics of the Morse oscillator, Chem Phys Letters, Vol 148, 397–403.
Herrick, D.R., Variable dimensionality in the group-theoretic prediction of configuration mixings for doubly-excited helium, J Math Phys, Vol 16, p 1046, 1975.
Herrick, D.R., New symmetry properties of atoms and molecules, Adv Chem Phys, Vol 52, p 1, 1983.
Herschbach, Dudley R., Dimensional interpolation for two-electron atoms, J Chem Phys, Vol 84, p 838, 1986.
Herschbach, Dudley R., Avery, John and Goscinski, Osvaldo, Eds., Dimensional Scaling in Chemical Physics, Kluwer, Dordrecht, 1993.
Hietschold, M.; Wonn, H. and Renz, G., Hartree-Fock-Slater exchange for anisotropic occupation in momentum space, Czech J Phys, Vol B 35(2), p 168–75, 1985.
Hillery, M., O’Connell, R.F., Scully, M.O., and Wigner, E.P., Distribution functions in physics: Fundementals, Physics Reports, Vol 106, 121–167, 1984.
Holoeien, E. and Midtdal, J., Variational nonrelativistic calculations for the (2pnp)1,3Pe states of two-electron atomic systems, J Phys B, Vol 4(10), p 1243–9, 1971.
Holz, J., Self-energy of electrons in a Coulomb field: momentum-space method, Z Phys D: At, Mol Clusters, Vol 4(3), p 211–25, 1987.
Horacek, Jiri and Zejda, Ladislav, Sturmian functions for nonlocal interactions, Czech J Phys, Vol 43(12), p 1191–201, 1993.
Hughs, J.W.B., Proc Phys Soc, Vol 91, p 810, 1967.
Hua, L.K., Harmonic Analysis of Functions of Several Complex Variables in the Classical Domains, American Mathematical Society, Providence, R.I., 1963.
Ihm, J.; Zunger, Alex and Cohen, Marvin L., Momentum-space formalism for the total energy of solids, J Phys C, Vol 12(21), p 4409–22, 1979.
Ishikawa, Yasuyuki; Rodriguez, Wilfredo and Alexander, S.A., Solution of the integral Dirac equation in momentum space, Int J Quantum Chem, Quantum Chem Symp, Vol 21, p 417–23, 1987.
Ishikawa, Yasuyuki; Rodriguez, Wilfredo; Torres, Samuel and Alexander S.A., Solving the Dirac equation in momentum space: a numerical study of hydrogen diatomic monopositive ion, Chem Phys Lett, Vol 143(3), p 289–92, 1988.
Jain, Ashok and Winter, Thomas G., Electron transfer, target excitation, and ionization in H+ + Na(3s) and H+ + Na(3p) collisions in the coupled-Sturmian-pseudostate approach, Phys Rev A: At, Mol, Opt Phys, Vol 51(4), p 2963–73, 1995.
Jain, Babu L., A numerical study on the choice of basis sets used for translating ETOs in multi-center LCA 0 calculations, ETO Multicent Mol Integr, Proc Int Conf, 1st, Reidel, Dordrecht, Neth, p 129–33, 81, Ed. Weatherford, Charles A.; Jones, Herbert W., 1982.
Jasperse, J.R., Method for one particle bound to two identical fixed centers: application to H +2 Phys Rev A, Vol (3)2(6), p 2232–44, 1970.
Jolicard, Georges and Billing, Gert Due, Energy dependence study of vibrational inelastic collisions using the wave operator theory and an analysis of quantum flows in momentum space, Chem Phys, Vol 149(3), p 261–73, 1991.
Judd, B.R., Angular Momentum Theory for Diatomic Molecules, Academic Press, New York, 1975.
Kaijser, Per and Lindner, Peter, Momentum distribution of diatomic molecules, Philos Mag, Vol 31(4), p 871–82, 1975.
Kaijser, Per and Sabin, John R., A comparison between the LCAOX. alpha. and Hartree-Fock wave functions for momentum space properties of ammonia, J Chem Phys, Vol 74(1), p 559–63, 1981.
Karule, E. and Pratt, R.H., Transformed Coulomb Green function Sturmian expansion, J Phys B: At, Mol Opt Phys, Vol 24(7), p 1585–91, 1991.
Katyurin, S.V. and Glinkin, O.G., Variation-iteration method for one-dimensional two-electron systems, Int J Quantum Chem, Vol 43(2), p 251–8, 1992.
Kellman, M.E. and Herrick, D.R., Ro-vibrational collective interpretation of supermultiplet classifications of intrashell levels of two-electron atoms, Phys Rev A, Vol 22, p 1536, 1980.
Kil’dyushov, M.S., Sov J Nucl Phys, Vol 15, p 113, 1972.
Kil’dyushov, M.S., and Kuznetsov, G.I., Sov. J. Nucl. Phys., Vol 17, p 1330, 1973.
King, H.F., Stanton, R.E., Kim, H., Wyatt, R.E., and Parr, R.G., J. Chem. Phys., Vol 47, p 1936, 1967.
Klar, H., J Phys B, Vol 7, L436, 1974.
Klar, H. and Klar, M., An accurate treatment of two-elecctron systems, J Phys B, Vol 13, p 1057, 1980.
Klar, H., Exact atomic wave functions-a generalized power-series expansion using hyperspherical coordinates, J Phys A, Vol 18, p 1561, 1985.
Klarsfeld, S. and Maquet, A., Analytic continuation of sturmian expansions for two-photon ionization, Phys Lett A, Vol 73A(2), p 100–2, 1979.
Klarsfeld, S. and Maquet, A., Pade-Sturmian approach to multi-photon ionization in hydrogenlike atoms, Phys Lett A, Vol 78A(1), p 40–2, 1980.
Klepikov, N.P., Sov. J. Nucl. Phys. Vol 19, p 462, 1974.
Knirk, D.L., Approach to the description of atoms using hyperspherical coordinates, J Chem Phys, Vol 60, p 1, 1974.
Koga Toshikatsu and Murai Takeshi, Energy-density relations in momentum space. III. Variational aspect, Theor Chim Acta, Vol 65(4), p 311–16, 1984.
Koga, Toshikatsu, Direct solution of the H(1s) H + long-range interactionproblem in momentum space, J Chem Phys, Vol 82, p 2022, 1985.
Koga, Toshikatsu and Matsumoto, S., An exact solution of the interaction problem between two ground-state hydrogen atoms, J Chem Phys, Vol 82, p 5127, 1985.
Koga, Toshikatsu and Kawaai, Ryousei, One-electron diatomics in momentum space. II. Second and third iterated LCAO solutions J Chem Phys, Vol 84(10), p 5651–4, 1986.
Koga, Toshikatsu and Matsuhashi, Toshiyuki, One-electron diatomics in momentum space. III. Nonvariational method for single-center expansion, J Chem Phys, Vol 87(3), p 1677–80, 1987.
Koga Toshikatsu and Matsuhashi Toshiyuki, Sum rules for nuclear attraction integrals over hydrogenic orbitals, J Chem Phys, Vol 87(8), p 4696–9, 1987.
Koga, Toshikatsu and Matsuhashi Toshiyuki, One-electron diatomics in momentum space. V. Nonvariational LCAO approaaach, J Chem Phys, Vol 89, p 983, 1988.
Koga, Toshikatsu; Yamamoto, Yoshiaki and Matsuhashi, Toshiyuki, One-electron diatomics in momentum space. IV. Floating single-center expansion, J Chem Phys, Vol 88(10), p 6675–6, 1988.
Koga, Toshikatsu and Ougihara, Tsutomu, One-electron diatomics in momentum space. VI. Nonvariational approach to excited states, J Chem Phys, Vol 91(2), p 1092–5, 1989.
Koga, Toshikatsu; Horiguchi, Takehide and Ishikawa, Yasuyuki, One-electron diatomics in momentum space. VII. Nonvariational approach to ground and excited states of heteronuclear systems, J Chem Phys, Vol 95(2), p 1086–9, 1991.
Kolos, W. and Wolniewicz, L., J. Chem. Phys., Vol 41, p 3663, 1964.
Kolos, W. and Wolniewicz, L., J. Chem. Phys., Vol 49, p 404, 1968.
Kramer, Paul J. and Chen, Joseph C.Y., Faddeev equations for atomic problems. IV. Convergence of the separable-expansion method for low-energy positron-hydrogen problems, Phys Rev A, Vol (3)3(2), p 568–73, 1971.
Krause, Jeffrey L. and Berry, R. Stephen, Electron correlation in alkaline earth atoms, Phys Rev A, Vol 31(5), p 3502–4, 1985.
Kristoffel, Nikolai, Statistics with arbitrary maximal allowed number of particles in the cell of the momentum space (methodical note), Eesti Tead Akad Toim, Fuus, Mat, Vol 41(3), p 207–10, 1992.
Kupperman, A. and Hypes, P.G., 3-dimensional quantum mechanical reactive scattering using symmetrized hyperspherical coordinates, J Chem Phys, Vol 84, 5962, 1986.
Kuznetsov, G.I. and Smorodinskii, Ya., Sov. J. Nucl. Phys., Vol 25, p 447, 1976.
Lakshmanan, M. and Hasegawa, H., On the canonical equivalence of the Kepler problem in coordinate and momentum spaces, J Phys A: Math Gen, Vol 17(16), 1984.
Landau, L.D., and Lifshitz, E.M., Quantum Mechanics; Non-Relativistic Theory, Pergamon Press, London, 1959.
Lassettre, Edwin N., Momentum eigenfunctions in the complex momentum plane. V. Analytic behavior of the Schrödinger equation in the complex momentum plane. The Yukawa potential, J Chem Phys, Vol 82(2), p 827–40, 1985.
Lassettre, Edwin N., Momentum eigenfunctions in the complex momentum plane. VI. A local potential function, J Chem Phys, Vol 83(4), p 1709–21, 1985.
Lin, C.D., Analytical channel functions for 2-electron atoms in hyperspherical coordinates, Phys. Rev. A, Vol 23, p 1585, 1981.
Linderberg, J. and Öhrn, Y., Kinetic energy functional in hyperspherical coordinates, Int J Quant Chem, Vol 27, p 273, 1985.
Liu, F.Q.; Hou, X.J. and Lim, T.K., Faddeev-Yakubovsky theory for four-body systems with three-body forces and its one-dimensional integral equations from the hyperspherical-harmonics expansion in momentum space, Few-Body Syst, Vol 4(2), p 89–101, 1988.
Liu, F.Q. and Lim, T.K., The hyperspherical-harmonics expansion method and the integral-equation approach to solving the few-body problem in momentum space, Few-Body Syst, Vol 5(1), p 31–43, 1988.
Lizengevich, A.I., Momentum correlations in a system of interacting particles, Ukr Fiz Zh (Russ Ed), Vol 33(10), p 1588–91, 1988.
López, R., Ramírez, G., Garcia de la Vega, J.M., and Fernández Rico, J., J Chim Phys, Vol 84, p 695, 1987.
Louck, J.D., Generalized orbital angular momentum and the n-fold degenerate quantum mechanical oscillator, J Mol Spectr, Vol 4, p 298, 1960.
Louck, J.D. and Galbraith, H.W., Rev Mod Phys, Vol 44, p 540, 1972.
Löwdin, P.O., Phys Rev Vol 97, p 1474, 1955.
Löwdin, P.O., Appl Phys Suppl, Vol 33, p 251, 1962.
McWeeny, Roy and Coulson, Charles A., The computation of wave functions in momentum space. I. The helium atom, Proc Phys Soc (London) A, Vol 62, p 509, 1949.
McWeeny, Roy, The computation of wave functions in momentum, space. II. The hydrogen molecule ion, Proc Phys Soc (London) A, Vol 62, p 509, 1949.
Manakov, N.L.; Rapoport, L.P. and Zapryagaev, S.A., Sturmian expansions of the relativistic Coulomb Green function, Phys Lett A, Vol 43(2), p 139–40, 1973.
Maquet, Alfred; Martin, Philippe and Veniard, Valerie, On the Coulomb Sturmian basis, NATO ASI Ser, Ser C, Vol 271 (Numer. Determ. Electron. Struct. At., Diat. Polyat. Mol.), p 295–9, 1989.
Maruani, Jean, editor, Molecules in Physics, Chemistry and Biology, Vol 3, Kluwer Academic Publishers, Dordrecht, 1989.
McCarthy, I.E. and Rossi, A.M., Momentum-space calculation of electron-molecule scattering, Phys Rev A: At, Mol, Opt Phys, Vol 49(6), p 4645–52, 1994.
McCarthy, I.E. and Stelbovics, A.T., The momentum-space coupled-channels-optical method for electron-atom scattering, Flinders Univ South Aust, Inst At Stud, (Tech Rep) FIAS-R, (FIAS-R-111,), p 51 pp., 1983.
Michels, M.A.J., Int. J. Quantum Chem., Vol 20, p 951, 1981.
Mizuno, J., Use of the Sturmian function for the calculation of the third harmonic generation coefficient of the hydrogen atom, J Phys B, Vol 5(6), p 1149–54, 1972.
Monkhorst, Hendrik J. and Harris, Frank E., Accurate calculation of Fourier transform of two-center Slater orbital products, Int J Quantum Chem, Vol 6, p 601, 1972.
Monkhorst, Hendrik J. and Jeziorski, Bogumil, No linear dependence or many-center integral problems in momentum space quantum chemistry, J Chem Phys, Vol 71(12), p 5268–9, 1979.
Moore, C.E., Atomic Energy Levels; Circular of the National Bureau of Standards 467, Superintendent of Documents, U.S. Government Printing Office, Washington 25 D.C., 1949.
Navasa, J. and Tsoucaris, G., Molecular wave functions an momentum space, Phys Rev A, Vol 24, p 683, 1981.
Nikiforov, A.F., Suslov, S.K., and Uvarov, V.B., Classical Orthogonal Polynomials of a Discrete Variable, Springer-Verlag, Berlin, 1991.
Norbury, John W.; Maung, Khin Maung and Kahana, David E., Exact numerical solution of the spinless Salpeter equation for the Coulomb potential in momentum space, Phys Rev A: At, Mol, Opt Phys, Vol 50(5), p 3609–13, 1994.
Novosadov, B.K., Opt Spectrosc, Vol 41, p 490, 1976.
Novosadov, B.K., Int J Quantum Chem, Vol 24, p 1, 1983.
Ojha, P.C., The Jacobi-matrix method in parabolic coordinates: expansion of Coulomb functions in parabolic Sturmians, J Math Phys (N Y), Vol 28(2), p 392–6, 1987.
Park, I1 Hung; Kim, Hong Ju and Kang, Ju Sang, Computer simulation of quantum mechanical scattering in coordinate and momentum space Sae Mulli, Vol 26(4), p 155–67, 1986.
Pathak, Rajeev K; Kulkarni, Sudhir A. and Gadre, Shridhar R., Momentum space atomic first-order density matrixes and “exchange-only” correlation factors, Phys Rev A, Vol 42(5), p 2622–6, 1990.
Pathak, Rajeev K; Panat, Padmakar V. and Gadre, Shridhar R., Local-density-functional model for atoms in momentum space, Phys Rev A, Vol 26(6), p 3073–7, 1982.
Pauling, L., and Wilson, E.B., Introduction to Quantum Mechanics, McGraw-Hill, 1935.
Pisani, L. and Clementi, E., in Methods and Techniques in Computational Chemistry, Clemennti, E., and Corongiu, G., Eds., STEF, Cagliari, 1995.
Plante, D.R., Johnson, W.R., and Sapirstein, J., Phys. Rev. Vol A49, p 3519, 1994.
Podolski, B., Proc. Natl. Acad. Sci. (USA), Vol 14, p 253, 1928.
Podolski, B. and Pauling, L., Phys Rev, Vol 34, p 109, 1929.
Potvliege, R.M. and Shakeshaft, Robin, Determination of the scattering matrix by use of the Sturmian representation of the wave function: choice of basis wave number, J Phys B: At, Mol Opt Phys, Vol 21(21), p L645, 1988.
Potvliege, R.M. and Smith, Philip H.G., Stabilization of excited states and harmonic generation: Recent theoretical results in the Sturmian-Floquet approach, NATO ASI Ser, Ser B, Vol 316 (Super-Intense Laser-Atom Physics), p 173–84, 1993.
Pyykkö, P., Relativistic Theory of Atoms and Molecules. A Bibliography, 1916–1985, Lecture Notes in Chemistry, Vol 41, 1986.
Pyykkö, P., Chem. Rev., Vol. 88, p 563, 1988.
Rahman, N.K., On the Sturmian representation of the Coulomb Green’s function in perturbation calculation, J Chem Phys, Vol 67(4), p 1684–5, 1977.
Rawitscher, G.H. and Delic, G., Sturmian, representation of the optical model potential due to coupling to inelastic channels, Phys Rev C, Vol 29(4), p 1153–62, 1984.
Rawitscher, George H. and Delic, George, Solution of the scattering T matrix equation in discrete complex momentum space, Phys Rev C, Vol 29(3), p 747–54, 1984.
Regier, Philip E.; Fisher, Jacob; Sharma, B.S. and Thakkar, Ajit J., Gaussian us. Slater representations of d orbitals: An information theoretic appraisal based on both position and momentum space properties, Int J Quantum Chem, Vol 28(4), p 429–49, 1985.
Ritchie, Burke, Comment on “Electron molecule scattering in momentum space”, J Chem Phys, vol 72(2), p 1420–1, 1980.
Ritchie, Burke, Electron-molecule scattering in momentum space, J Chem Phys, Vol 70(6), p 2663–9, 1979.
Rodriguez, Wilfredo and Ishikawa, Yasuyuki, Fully numerical solutions of the Hartree-Fock equation in momentum space: a numerical study of the helium atom and the hydrogen diatomic monopositive ion, Int J Quantum Chem, Quantum Chem Symp, Vol 22, p 445–56, 1988.
Rodriguez, Wilfredo and Ishikawa, Yasuyuki, Fully numerical solutions of the molecular Schrödinger equation in momentum space, Chem Phys Lett, Vol 146(6), p 515–17, 1988.
Rohwedder, Bernd and Englert, Berthold Georg, Semiclassical quantization in momentum space, Phys Rev A: At, Mol, Opt Phys, Vol 49(4), p 2340–6, 1994.
Rotenberg, Manuel, Ann. Phys. (New York), Vol 19, p 262, 1962.
Rotenberg, Manuel, Theory and application of Sturmian functions, Adv. At. Mol. Phys., Vol 6, p 233–68, 1970.
Royer, A., Wigner function as the expectation value of a parity operator, Phys Rev A, Vol 15, p 449–450, 1977.
Rudin, W., Fourier Analysis on Groups, Interscience, New York, 1962.
Schmider, Hartmut; Smith, Vedene H. Jr. and Weyrich, Wolf, On the inference of the one-particle density matrix from position and momentum-space form factors, Z Naturforsch, A: Phys Sci, Vol 48(1–2), p 211–20, 1993.
Schmidcr, Hartmut; Smith, Vedene H. Jr. and Weyrich, Wolf, Reconstruction of the one-particle density matrix from expectation values in position and momentum space, J Chem Phys, Vol 96(12), p 8986–94, 1992.
Schuch, Dieter, On a form of nonlinear dissipative wave mechanics valid in position-and momentum-space, Int J Quantum Chem, Quantum Chem Symp, Vol 28 (Proceedings of the International Symposium on Atomic, Molecular, and Condensed Matter Theory and Computational Methods, 1994), p 251–9, 1994.
Shabaev, V.M., Relativistic Coulomb Green function with regard to finite size of the nucleus, Vestn Leningr Univ, Fiz, Khim (2), p 92–6, 1984.
Shakeshaft, Robin and Tang, X., Determination of the scattering matrix by use of the Sturmian representation of the wave function, Phys Rev A: Gen Phys, Vol 35(9), p 3945–8, 1987.
Shakeshaft, Robin, A note on the Sturmian expansion of the Coulomb Green.s function. J Phys B: At Mol Phys, Vol 18(17), p L611–L615, 1985.
Shakeshaft, Robin, Application of the Sturmian expansion to multiphoton absorption:: hydrogen above the ionization thresho1d, Phys Rev A: Gen Phys, Vol 34(6), p 5119–22, 1986.
Shakeshaft, Robin, Coupled-state calculations of proton-hydrogen,-atom scattering with a Sturmian, expansion, Phys Rev A, Vol 14(5),p 1626–33, 1976.
Shakeshaft,, Robin, Sturmian expansion of Green’s function and its application to multiphoton ionization of hydrogen, Phys Rev A: Gen Phys, Vol 34(1), p 244–52, 1986.
Shakeshaft, Robin, Sturmian basis functions in the coupled state impact parameter method for hydrogen(+) + atomic hydrogen scattering, J Phys B, Vol 8(7), p 1114–28, 1975.
Shelton, D.P., Hyperpolarizability of the hydrogen atom, Phys Rev A: Gen Phys, Vol 36(7), p 3032–41, 1987.
Sherstyuk, A.I., Sturmian expansions in the many-, fermion problem, Teor Mat Fiz, Vol 56(2), p 272–87, 1983.
Shibuya, T. and Wulfman, C.E., Molecular orbitals in momentum space, Proc Roy Soc A, Vol 286, p 376, 1965.
Shull, H. and Löwdin, P.-O., Superposition of configurations and natural spin-orbitals. Applications to the He problem, J Chem Phys, Vol 30, p 617, 1959
Simas, Alfredo M.; Thakkar, Ajit J. and Smith, Vedene H. Jr., Momentum space properties of various orbital basis sets used in quantum chemical calculations, Int J Quantum Chem, Vol 21(2), p 419–29, 1982.
Sloan, I.H. and Gray, J.D., Separable expansions of the t-matrix, Phys Lett B, Vol 44(4), p 354–6, 1973.
Sloan, Ian H., Sturmian expansion of the Coulomb t matrix, Phys Rev A, Vol 7(3), p 1016–23, 1973.
Smirnov, Yu. F. and Shitikova, K.V., Sov J Part Nucl, Vol 8, p344, 1976.
Smith, F.T., Generalized angular momentum in many-body collisions, Phys Rev, Vol 120, p 1058, 1960.
Smith, F.T., A symmetric representation for three-body problems. I. Motion in a plane, J Math Phys, Vol 3, p 735, 1962.
Smith, F.T., Participation of vibration in exchange reactions, J Chem Phys, Vol 31, p 1352–1359, 1959.
Smith, Vedene H. Jr., Density functional theory and local potential approximations from momentum space considerations, Local Density Approximations Quantum Chem Solid State Phys, (Proc Symp), Plenum, New York, N. Y, p 1–19, 82, Eds. Dahl, Jens Peder; Avery, John, 1984.
Smorodinskii, Ya., and Efros, V.D., Sov. J. Nucl. Phys. Vol 17, p 210, 1973.
Springborg, M. and Dahl, J.P., Wigner’s phase-space function and atomic structure, Phys Rev A, Vol 36, p 1050–1062, 1987.
Szmytkomski, R., The Dirac-Coulomb Sturmians and the Series Expansion of the Dirac-Coulomb Green Function; Application to the Relativistic Polarizability of the Hydrogenlike Atom, J. Phys. A, Vol 31, p 4963, 1998.
Szmytkowski, R., The Continuum Schrödinger-Coulomb and Dirac-Coulomb Sturmian Functions, J. Phys. A, Vol 31, p 4963, 1998.
Szmytkowski, R., The Continuum Schrödinger-Coulomb and Dirac-Coulomb Sturmian Functions, J. Phys. A, Vol 31, p 4963, 1998.
Taieb, Richard; Veniard, Valerie; Maquet, Alfred; Vucic S. and Potvliege R.M., Light polarization effects in laser-assisted electronimpact-ionization ((e, 2e)) collisions: a Sturmian approach, J Phys B: At, Mol Opt Phys, Vol 24(14), p 3229–40, 1991.
Tang, X. and Shakeshaft, R., A note on the solution of the Schrödinger equation in momentum space, Z Phys D: At, Mol Clusters, Vol 6(a), p 113–17, 1987.
Tarter, C.B., J Math Phys, Vol 11, p 3192, 1970.
Tel-nov, D.A., The d.c. Stark effect in a hydrogen atom via Sturmian expansions, J Phys B: At, Mol Opt Phys, Vol 22(14), p L399–L404, 1989.
Thakkar, Ajit J. and Koga, Toshikatsu, Analytic approximations to the momentum moments of neutral atoms, Int J Quantum Chem, Quantum Chem Symp, Vol 26 (Proc. Int. Symp. At., Mol., Condens. Matter Theory Comput. Methods, 1992), p 291–8, 1992.
Thakkar, Ajit J. and Tatewaki, Hiroshi, Momentum-space properties of nitrogen: improved configuration-interaction calculations, Phys Rev A, Vol 42(3), p 1336–45, 1990.
Tzara, C., A study of the relativistic Coulomb problem in momentum space, Phys Lett A, Vol 111A(7), p 343–8, 1985.
Ugalde, Jesus M., Exchange-correlation effects in momentum space for atoms: an analysis of the isoelectronic series of lithium 2S and beryllium 1S, J Phys B: At Mol Phys, Vol 20(10), p 2153–63, 1987.
Van Haeringen, H. and Kok, L.P., Inequalities for and zeros of the Coulomb T matrix in momentum space, Few Body Probl Phys, Proc Int IUPAP Conf, 10th, North-Holland, Amsterdam, Neth, p 361–2, 83, Ed. Zeitnitz, Bernhard, 1984.
Vilenkin, N.K., Special Functions and the Theory of Group Representations, American Mathematical Society, Proovidence, R.I., 1968.
Vilenkin, N. Ya.; Kuznetsov, G.I., and Smorodinskii, Ya.A., Sov J Nucl Phys, Vol 2, p 645, 1966.
Vladimirov, Yu.S. and Kislov, V.V., Charge of the nucleus of a hydrogen-like atom as an eigenvalue of a 6-dimensional wave equation in momentum space, Izv Vyssh Uchebn Zaved, Fiz, Vol 28(4), p 66–9, 1985.
Weatherford, Charles A., Scaled hydrogenic Sturmians as ETOs, ETO Multicent Mol Integr, Proc Int Conf, 1st, Reidel, Dordrecht, Neth, p 29–34, 81, Ed. Weatherford, Charles A.; Jones, Herbert W., 1982.
Wen, Zhen-Yi and Avery, John, Some properties of hyperspherical harmonics, J Math Phys, Vol 26, 396, 1985.
Weniger, E.J., Weakly convergent expansions of a plane wave and their use in Fourier integrals, J Math Phys, Vol 26, p 276, 1985.
Weniger, E.J. and Steinborn, E.O., The Fourier transforms of some exponential-type basis functions and their relevance for multicenter problems, J. Chem Phys, Vol 78, p 6121, 1983.
Weniger, E.J.; Grotendorst, J., and Steinborn, E.O., Unified analytical treatment of overlap, two-center nuclear attraction, and Coulomb integrals of B functions via the Fourier transform method, Phys Rev A, Vol 33, p 3688, 1986.
Whitten, R.C. and Sims, J.S., Phys Rev A, Vol 9, p 1586, 1974.
Wigner, E., Phys Rev, Vol 40, p 749, 1932.
Windt, Laurent de; Fischer, Patrick; Defranceschi, Mireille; Delhalle, Joseph and Fripiat, Joseph G., A combined analytical and numerical strategy to solve the atomic Hartree-Fock equations in momentum space, J Comput Phys, Vol 111(2), p 266–74, 1994.
Winter, Thomas G. and Alston, Steven G., Coupled-Sturmian and perturbative treatments of electron transfer and ionization in high-energy helium p-He+ collisions, Phys Rev A, Vol 45(3), p 1562–8, 1992.
Winter, Thomas G., Electron transfer and ionization in collisions between protons and the ions lithium(2+) and helium(1+) studied with the use of a Sturmian basis, Phys Rev A: Gen Phys, Vol 33(6), p 3842–52, 1986.
Winter, Thomas G., Coupled-Sturmian treatment of electron transfer and ionization in proton-neon collisions, Phys Rev A, Vol 48(5), p 3706–13, 1993.
Winter, Thomas G., Electron transfer and ionization in collisions between protons and the ions helium(1+), lithium(2+), beryllium(3+), boron(4+), and carbon(5+) studied with the use of a Sturmian basis, Phys Rev A: Gen Phys, Vol 35(9), p 3799–809, 1987.
Winter, Thomas G., Electron transfer in p-helium(1+) ion and helium(2+) ion-atomic helium collisions using a Sturmian basis, Phys Rev A, Vol 25(a), p 697–712, 1982.
Winter, Thomas G., Sturmian treatment of excitation and ionization in high-energy proton-helium collisions, Phys Rev A, Vol 43(9), p 4727–35, 1991.
Winter, Thomas G., Coupled-Sturmian treatment of electron transfer and ionization in proton-carbon collisions, Phys Rev A, Vol 47(1), p 264–72, 1993.
Winter, Thomas G., Electron transfer and ionization in proton-helium collisions studied using a Sturmian basis, Phys Rev A, Vol 44(7), p 4353–67, 1991.
Wulfman, Carl E., Semiquantitative united-atom treatment and the shape of triatomic molecules, J Chem Phys Vol 31, p 381, 1959.
Wulfman, Carl E., Dynamical groups an atomic and molecular physics, in Group Theory and its Applications, Loebel, E.M. Ed., Academic Press, 1971.
Wulfman, Carl E., Approximate dynamical symmetry of two-electron atoms, Chem Phys Letters Vol 23(3), 1973.
Wulfman, Carl E., On the space of eigenvectors in molecular quantum mechanics, Int J Quant Chem Vol 49, p 185, 1994.
Yurtsever, Ersin; Yilmaz, Osman and Shillady, D.D., Sturmian basis matrix solution of vibrational potentials. Chem Phys Lett, Vol 85(1), p 111–16, 1982.
Yurtsever, Ersin, Franck-Condon integrals over a sturmian basis. An application to photoelectron spectra of molecular hydrogen and molecular nitrogen, Chem Phys Lett, Vol 91(1), p 21–6, 1982.
Rights and permissions
Copyright information
© 2002 Kluwer Academic Publishers
About this chapter
Cite this chapter
(2002). Relativistic Effects. In: Hyperspherical Harmonics and Generalized Sturmians. Progress in Theoretical Chemistry and Physics, vol 4. Springer, Dordrecht. https://doi.org/10.1007/0-306-46944-8_8
Download citation
DOI: https://doi.org/10.1007/0-306-46944-8_8
Publisher Name: Springer, Dordrecht
Print ISBN: 978-0-7923-6087-2
Online ISBN: 978-0-306-46944-2
eBook Packages: Springer Book Archive