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Group Theory and the Harmonic Oscillator: The Work of Marcos Moshinsky

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Book cover Symmetries in Physics

Abstract

Physics in Mexico is very young. Only a handful of papers had been published in the international literature by Mexican physicists before the end of World War II. It is therefore not difficult to imagine the scientific desert Marcos Moshinsky found after returning from Princeton in 1949. Nevertheless he started publishing work of good quality already in 1950 and has done so ever since for the following 41 years, including the present 1991 when we are celebrating his seventieth anniversary.

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References

  1. Problemas de condiciones a la frontera de características discontinuas. Bol. Soc. Mat. Mex. 4, 1 (1947).

    Google Scholar 

  2. Relativistic interactions by means of boundary conditions. Ph.D Dissertation, Princeton University (1949).

    Google Scholar 

  3. Vibración de una membrana circular de dos densidades. Rev. Ing. Hid. 3, 5 (1949).

    Google Scholar 

  4. Interference phenomena for particles obeying Bose or Fermi statistics. Proc. A. Phil. Soc. 94, 53 (1950).

    Google Scholar 

  5. Interactions of Birkhoff’s gravitational field with the electromagnetic and pair fields. Phys. Rev. 80, 514, (1950).

    Google Scholar 

  6. Auto-adjunticidad de problemas vectoriales de condiciones a la frontera. Bol. Soc. Mat. Mex. 7, 1 (1950).

    Google Scholar 

  7. Boundary conditions for the description of nuclear reactions. Phys. Rev. 81, 347 (1951).

    Google Scholar 

  8. Boundary conditions and time dependent states. Phys. Rev. 84, 525 (1951).

    Google Scholar 

  9. Quantum mechanics in Fock space. Phys. Rev. 84, 533 (1951).

    Google Scholar 

  10. Efectos transitorios en la dispersión por una esfera rígida. Rev. Mex. Fís. 1, 29 (1952).

    Google Scholar 

  11. Sobre una clase de transformadas de interés en la dispersión nuclear. Rev. Mex. Fís. 1, 114 (1952).

    Google Scholar 

  12. Diffraction in time. Phys. Rev. 88, 625 (1952).

    Google Scholar 

  13. On a dynamical theory of scattering. In: Novas Técnicas de Pesquisa en Física. Academia Brasileira de Ciencias (1954), pp. 279–285.

    Google Scholar 

  14. Difracción en el tiempo y la ecuación de Dirac. Rev. Mex. Fís. 1, 151 (1952).

    Google Scholar 

  15. On matrix boundary value problems [with J. Adem]. Quart. App. Math. 9, 424 (1952).

    Google Scholar 

  16. Dispersión de neutrones por cristales en vibración. Rev. Mex. Fís. 2, 137 (1953).

    Google Scholar 

  17. Poles of the S matrix for resonance reactions. Phys. Rev. 91, 984 (1953).

    Google Scholar 

  18. Reacciones nucleares entre partícular con carga. Rev. Mex. Fís. 2, 244 (1953).

    Google Scholar 

  19. Vibraciones térmicas de los cristales y la difracción de neutrones. Rev. Mex. Fís. 3, 1 (1954).

    Google Scholar 

  20. Polos de la función S para dispersión de momento angular arbitrario. Ann. Acad. Brasileira de Ciencias, 25, 343 (1953).

    Google Scholar 

  21. Description de la diffraction-hachage par une distribution de sources. C.R. Acad. Sci. Paris, 283, 2395 (1954).

    Google Scholar 

  22. Definition et propriétés analytiques des matrices R et S associées aux forces tensorielles. I. Cas de la matrices R [with W. Laskar]. C.R. Acad. Sci. Paris, 283, 2496 (1954).

    Google Scholar 

  23. II. Cas de la matrice S [with W. Laskar]. C.R. Acad. Sci. Paris, 239, 29 (1954).

    Google Scholar 

  24. Forces tensoriélles dépendant de la vitesse. J. de Phys. et Radium. 15, 264 (1954).

    Google Scholar 

  25. Difracción en el tiempo asociada a una distribución de fuentes. Rev. Mex. Fís. 3, 236(1954).

    Google Scholar 

  26. Dispersión de ondas sonoras por una gota de líquido. Rev. Mex. Fís. 4, 95 (1955).

    Google Scholar 

  27. Movimientos colectivos y las reacciones nucleares. Rev. Mex. Fís. 5, 1 (1956).

    Google Scholar 

  28. Collective motions in nuclei [with A.M. Mailman]. Notes on the Summer Course in Theoretical Nuclear Physics (1956).

    Google Scholar 

  29. Velocity dependent forces and nuclear structure. I. Central forces. Phys. Rev. 106, 117 (1957).

    Google Scholar 

  30. Repulsive core and nuclear shell theory [with M. Bauer]. Nuclear Physics 4, 615 (1957).

    Google Scholar 

  31. Fuerzas nucleares con centro repulsivo y el modelo de capas del núcleo. Efectos de segundo orden. Rev. Mex. Fís. 6, 185 (1957).

    Google Scholar 

  32. Velocity dependent forces and nuclear structure. II. Spin dependent forces. Phys. Rev. 109, 933 (1958).

    Google Scholar 

  33. Short range forces and nuclear shell theory. Nucl. Phys. 8, 19 (1958).

    Google Scholar 

  34. La interacción spin-órbita entre nucleones y el acoplamiento spinórbita en el modelo de capas del núcleo. Rev. Mex. Fís. 7, 95 (1958).

    Google Scholar 

  35. Transformation brackets for harmonic oscillator functions. Nucl. Phys. 13, 104 (1959).

    Google Scholar 

  36. Matrix elements in nuclear shell theory. Nucl. Phys. 17, 16 (1960).

    Google Scholar 

  37. Invariance principles and beta decay [with C.A. Mallmann and J. de Oyarzábal], Notes of the Latin American school of Physics (1959).

    Google Scholar 

  38. Group theory of harmonic oscillators. I. The collective modes [with V. Bargmann]. Nuclear Phys. 18, 697 (1960).

    Google Scholar 

  39. Tables of transformation brackets [with T.A. Brody] Monografías del Instituto de Física (1960). Reprinted by Gordon & Breach (1969).

    Google Scholar 

  40. Group theory of harmonic oscillators. II. The integrals of motion of the quadrupole-quadrupole interaction [with V. Bargmann]. Nucl. Phys. 23, 177 (1961).

    Google Scholar 

  41. Dispersion relations and the causality concept. [with J.M. Lozano]. N. Cimento 20, 59 (1961).

    Google Scholar 

  42. Simetrías y reglas de suma de los paréntesis de transformación [with T.A. Brody]. Rev. Mex. Fís. 9, 181 (1960).

    Google Scholar 

  43. On exact solutions for the pairing plus quadrupole-quadrupole interactions. Proceedings of the Rutherford Jubilee Conference (1961).

    Google Scholar 

  44. The harmonic oscillator and supermultiplet theory. I. The single shell picture. Nucl. Phys. 31, 384 (1962).

    Google Scholar 

  45. A soluble many body problem for particles in a Coulomb field. Phys. Rev. 126, 1880 (1962).

    Google Scholar 

  46. Estudio teórico de los niveles de Ne20 [with E. Chacón]. 4° Simposio de Energía Nuclear (1962). Translation: Theoretical analysis of the energy levels in Ne20. Phys. Lett 1, 330 (1962).

    Google Scholar 

  47. Wigner coefficients for the SU 3 group and some applications. Rev. Mod. Phys. 34, 813 (1962).

    Google Scholar 

  48. Bases for the irreducible representations of the unitary groups and some applications. J. Math. Phys. 4, 1128 (1963).

    Google Scholar 

  49. Complete classification of states of supermultiplets theory [with J. Nagel]. Phys. Lett 5, 173 (1963).

    Google Scholar 

  50. Group theory and many body problems with finite number of states. Phys. Lett. 6, 305 (1963).

    Google Scholar 

  51. Group theory and collective motions. Notes of the Latin American School of Physics (1962).

    Google Scholar 

  52. Group theoretical methods and a model interaction in nuclear shell theory. Proceedings of the International Conference on Nuclear Physics (1964).

    Google Scholar 

  53. Operators that lower or raise the irreducible vector space of U n [with J. Nagel]. J. Math. Phys. 6, 682 (1965).

    Google Scholar 

  54. Normalization coefficients for lowering and raising operators and the matrix elements of the generators of U n [with J. Nagel]. Rev. Mex. Fís. 14, 29 (1965).

    Google Scholar 

  55. The three body problems and the SU 4 group [with E. Chacón]. Rev. Mex. Fís. 14, 119 (1965).

    Google Scholar 

  56. Recurrence relations for the Wigner coefficients of unitary groups [with T.A. Brody and I. Renero]. J. Math. Phys. 6, 1540 (1965).

    Google Scholar 

  57. Gel’fand states and the irreducible representations of the symmetric group. J. Math. Phys. 7, 691 (1966).

    Google Scholar 

  58. Group theory of harmonic oscillators. III. States with permutational symmetry [with P. Kramer]. Nuclear Physics 82, 241 (1966).

    Google Scholar 

  59. Group theory and nuclear structure in the 2s–1d-shell [with M. Berrondo and J. Pineda]. Proceedings of the Second Conference on Structure of Light and Medium Nuclei (U. of Kansas, 1967).

    Google Scholar 

  60. Studies on nuclear structure in the 2s–1d-shell. III. Group theory and particle hole states [with J. Flores]. Nucl Phys. A93, 81 (1967).

    Google Scholar 

  61. Group theory and the many body problems. In: Physics of Many Particle Systems, (Gordon & Breach, 1966); reproduced in expanded book form with the same title by Gordon & Breach (1967).

    Google Scholar 

  62. Some matrix elements and normalization coefficients in SU n [with T.A. Brody and I. Renero]. Rev. Mex. Fís. 15, 145 (1966).

    Google Scholar 

  63. Group theory of harmonic oscillators and nuclear structure [with P. Kramer]. In: Group Theory and Applications. Ed. by E.M. Loebl (Academic Press, 1968).

    Google Scholar 

  64. Representation of finite U 3 transformations [with E. Chacón]. Phys. Lett. 23, 567 (1966).

    Google Scholar 

  65. Energy levels of the 4 nucleon system [with P. Kramer]. Phys. Lett. 23, 574 (1966).

    Google Scholar 

  66. Group theory of harmonic oscillators. IV. Dynamics of the two, three and four particle problem [with P. Kramer]. Nucl. Phys. A107, 481 (1968).

    Google Scholar 

  67. Racah coefficients and states with permutational symmetry [with E. Chacón]. In: Racah Memorial Volume (North Holland Publishing Co., 1968).

    Google Scholar 

  68. The harmonic oscillator in atomic and molecular physics. I. General approach and application to atoms and molecules of up to 4 electrons [with O. Novaro]. J. Chem. Phys. 48, 4162 (1968).

    Google Scholar 

  69. Group theory and nuclear structure. Lectures Notes (ICTP, 1967). In: Fundamentals of Nuclear Theory (IAEA, 1967).

    Google Scholar 

  70. How good is the Hartree-Fock approximation? Am. J. Phys. 36, 52 (1967).

    Google Scholar 

  71. A general approach to fractional parentage coefficients [with V. Syamala Devi]. J. Math. Phys. 10, 455 (1969).

    Google Scholar 

  72. Group theory and nuclear structure in the 2s–1d-shell. Proceedings of the Tokyo Conference on Nuclear Structure (1967).

    Google Scholar 

  73. How good is the Born-Oppenheimer approximation? [with C. Kittel] Proc. Natl. Acad. Sci. 60, 1110 (1968).

    Google Scholar 

  74. Harmonic oscillator states for three particle systems. Applications to the form factor of the proton as a system of three quarks [with V.C. Aguilera-Navarro and W. Yeh]. Rev. Mex. Fís. 4, 241 (1968).

    Google Scholar 

  75. Harmonic oscillator states and the α particle. I. Form factor for symmetric states in configuration space. Ann. Phys. 51, 312 (1969).

    Google Scholar 

  76. Harmonic oscillator states and the α particle. II. Configuration space states of arbitrary symmetry [with P. Kramer and V.C. Aguilera-Navarro]. Ann. Phys. 54, 379 (1969).

    Google Scholar 

  77. The Harmonic Oscillator in Modern Physics: From Atoms to Quarks. Gordon & Breach, New York (1969). Russian Translation (MIR, 1972).

    Google Scholar 

  78. Group theory of harmonic oscillators. V. The harmonic oscillator shell model [with P. Kramer]. Nucl. Phys. A125, 321 (1969).

    Google Scholar 

  79. Mechanical models for reactions involving isobaric analogue and doorway states [with P.A. Mello]. Am. J. Phys. 39, 54 (1971).

    Google Scholar 

  80. Generalization to arbitrary groups of the relations between seniority and quasispin [with C. Quesne]. Phys. Lett. 29B, 482 (1971).

    Google Scholar 

  81. How good is the Hartree-Fock approximation? II. The case of closed shells [with A. Calles]. Am. J. Phys. 38, 456 (1970).

    Google Scholar 

  82. Non-invariance groups in the second quantization picture and their applications [with C. Quesne]. J. Math. Phys. 11, 5 (1970).

    Google Scholar 

  83. The pseudo-atom, a soluble many body problem [with O. Novaro and A. Calles]. J. de Physique 31, 125 (1970).

    Google Scholar 

  84. Time dependent behavior of a classical model for reactions involving isobaric analogue states [with P.A. Mello]. Rev. Mex. Fís. 19, 157 (1970).

    Google Scholar 

  85. Oscillator systems [with C. Quesne]. Proceedings of the XV Solvay Conference, (Brussels, 1971).

    Google Scholar 

  86. Group theory and second quantization for non-orthogonal orbitals [with T.H. Seligman]. Ann. Phys. 66, 311 (1971).

    Google Scholar 

  87. 0(4) and U(3) symmetry breaking in the 2s–2p-shell [with E. Chacón, O. Novaro and C. Wulfman]. Phys. Rev. 3, 166 (1971).

    Google Scholar 

  88. Correlation effects in the α particle [with V.C. Aguilera-Navarro]. Phys. Lett 32B, 336 (1970).

    Google Scholar 

  89. Transformation brackets for three and four nucleon systems. Proceedings of the Conference on Clustering Phenomena. Bochum (IAEA, 1969).

    Google Scholar 

  90. Group theory and the few nucleon problem. In: 1968 Cargese Lectures (Gordon & Breach, 1969).

    Google Scholar 

  91. Applications of group theory to problems of atomic physics. In: New Directions of Atomic Physics (Yale University Press 1971).

    Google Scholar 

  92. Linear canonical transformations and their unitary representation [with C. Quesne]. J. Math. Phys. 12, 1772 (1971).

    Google Scholar 

  93. The charge form factor of the mass-3 nuclei [with C. Quesne and A.D. Jackson]. Rev. Mex. Fís. 20, 43 (1971).

    Google Scholar 

  94. Canonical transformations and matrix elements [with C. Quesne]. J. Math. Phys. 12, 1780 (1971).

    Google Scholar 

  95. Schematic theory for isobaric analogue states [with P.A. Mello]. Rev. Mex. Fís. 19, 339 (1970).

    Google Scholar 

  96. Implications of classical ergodicity in quantum mechanics [with P.A. Mello]. Ann. Phys. 71, 1 (1972).

    Google Scholar 

  97. Canonical transformations and quantum mechanics. Notes of the Latin American School of Physics (México, 1971).

    Google Scholar 

  98. Canonical transformations and the radial oscillator and Coulomb problems [with T.H. Seligman and K.B. Wolf]. J. Math. Phys. 13, 901 (1972).

    Google Scholar 

  99. Test of the many electron theory of atoms in an exactly solvable model [with A. Calles and O. Sinanoğlu]. Phys. Lett 40A, 79 (1972).

    Google Scholar 

  100. Canonical transformations and quantum mechanics. SIAM J. Appl. Math. 25, 193 (1973).

    Google Scholar 

  101. Comments on charge distribution in multipion production [with E. Chacón]. Phys. Rev. D7, 2783 (1973).

    Google Scholar 

  102. Canonical transformations and accidental degeneracy. I. The anisotropic oscillator [with J.D. Louck and K.B. Wolf]. J. Math. Phys. 14, 692 (1973).

    Google Scholar 

  103. Canonical transformations and accidental degeneracy. II. The isotropic oscillator in a sector [with J.D. Louck and K.B. Wolf]. J. Math. Phys. 14, 696 (1973).

    Google Scholar 

  104. Relation between hyperspherical and harmonic oscillator many-body matrix elements [with D. Levi]. N. Cimenio 204, 107 (1974).

    Google Scholar 

  105. An application of linear canonical transformations: Coherent states [with P.A. Mello]. Rev. Mex. Fís. 22, 257 (1973).

    Google Scholar 

  106. Relation between the hyperspherical harmonic and the harmonic oscillator method for the three body problem [with E. Chacón and D. Levi]. Rev. Mex. Fís. 22, 291 (1973).

    Google Scholar 

  107. Isotopic spin conservation and charge distribution in multipion production [with J. Patera, R.T. Sharp, and P. Winternitz]. Phys. Rev. D10, 1587 (1974).

    Google Scholar 

  108. Canonical transformations and accidental degeneracy. III. A unified approach to the problem [with J. Patera and P. Winternitz]. J. Math. Phys. 16, 82 (1975).

    Google Scholar 

  109. Complex extensions of canonical transformations and quantum mechanics [with P. Kramer and T.H. Seligman]. Group Theory its Applications Ed. by E.M. Loebl. Academic Press, (1975).

    Google Scholar 

  110. Lie Algebras in the Heisenberg and Schrödinger pictures and two body matrix elements. Proceedings of the 3rd Conference of Group Theoretical Methods in Physics (Marseille, 1973).

    Google Scholar 

  111. Nonlinear canonical transformations and their representation in quantum mechanics [with P.A. Mello]. J. Math. Phys. 16, 2017 (1975).

    Google Scholar 

  112. Canonical transformation and accidental degeneracy. IV. Problems with continuous spectra [with J. Patera]. J. Math. Phys. 16, 1866 (1975).

    Google Scholar 

  113. Equivalence of a class of Wigner coefficients of SU (1, 1) with those of SU(2) [with E. Chacón and D. Levi]. J. Math. Phys. 16, 1876 (1975).

    Google Scholar 

  114. Everything you ever wanted to know about SU(3) ⊃ O(3) [with J. Patera, R.T. Sharp, and P. Winternitz]. Ann. Phys. 95, 139 (1975).

    Google Scholar 

  115. U(5) ⊃ O(5) ⊃ 0(3) and the exact solution of the problem of quadruple vibrations of the nucleus [with E. Chacón and R.T. Sharp]. J. Math. Phys. 17, 668 (1976).

    Google Scholar 

  116. Canonical transformations and their representations in quantum mechanics. Proceedings of the Bonn Conference on Geometrical Quantization (1976).

    Google Scholar 

  117. Diffraction in time and the time-energy uncertainty relation. Am. J. Phys. 44, 1037 (1976).

    Google Scholar 

  118. Lie Algebras in the Schrodinger picture and radial integrals [with E. Chacón and D. Levi]. J. Math. Phys. 17, 1919 (1976).

    Google Scholar 

  119. Group theory of the collective model of the nucleus [with E. Chacón]. J. Math. Phys. 18, 870 (1977).

    Google Scholar 

  120. Non-bijective canonical transformations and their representation in quantum mechanics [with P. Kramer and T.H. Seligman]. J. Math. Phys. 19, 683 (1978).

    Google Scholar 

  121. Ambiguities in canonical transformations of classical systems and the spectra of quantum observables [with T. H. Seligman]. Proceedings of the 1977 Bonn Conference on Differential Geometric Methods in Mathematical Physics (Springer Verlag, 1978).

    Google Scholar 

  122. The gradient formula for the O(5) ⊃ O(3) chain of groups [with O. Castaños and A. Frank]. J. Math. Phys. 19, 1781 (1978).

    Google Scholar 

  123. Canonical trasnformations to action and angle variables and their representation in quantum mechanics [with T.H. Seligman]. Ann. Phys. 114, 243 (1978).

    Google Scholar 

  124. Group theory of the interacting boson model of the nucleus [with O. Castaños, E. Chacón, and A. Frank]. J. Math. Phys. 20, 35 (1979).

    Google Scholar 

  125. Group theory of the collective model of the nucleus. Proceedings of the Nuclear Physics Conference (Oaxtepec, 1978).

    Google Scholar 

  126. Nuclear reactions with collective degree of freedom [with E. Aguilera, O. Castaños, and A. Frank]. Proceedings of the Nuclear Physics Conference (Oaxtepec, 1978).

    Google Scholar 

  127. Canonical transformations to action and angle variables and their representation in quantum mechanics. II. The Coulomb problem [with T.H. Seligman]. Ann. Phys. 120, 430 (1979).

    Google Scholar 

  128. The ambiguity group for canonical transformations in classical mechanics [with T. H. Seligman]. Proceedings of the Conference on Group Theory and Applications, Austin, Texas. Springer-Verlag, Lecture Notes in Physics, Vol. 97 (1979).

    Google Scholar 

  129. Quadratic Hamiltonians in phase space and their eigenstates [with P. Winternitz]. J. Math. Phys. 21, 1667 (1980).

    Google Scholar 

  130. Irreducible decomposition of the direct products of q arbitrary representations of the symplectic group Sp(2n) and its relation with the orthogonal group O(q) [with E. Chacón and P. Winternitz]. Kinam 1, 259 (1979).

    Google Scholar 

  131. Canonical transformations to action and angle variables and their representation [with T.H. Seligman]. J Phys. A.: Math. Gen 12, L135 (1979).

    Google Scholar 

  132. Canonical transformations to action and angle variables. III. The general problem [with T.H. Seligman and J. Deenen]. Ann. Phys. (N.Y.) 127, 58 (1980).

    Google Scholar 

  133. Confrontation of nuclear collective models. Nucl. Phys. A338, 156 (1980).

    Google Scholar 

  134. Decay of a compound particle and the Einstein, Podolsky, and Rosen argument [with J. Flores, E. Henestroza, and P.A. Mello]. Am. J. Phys. 49, 59 (1981).

    Google Scholar 

  135. Wigner distribution functions and the representation of canonical transformations in quantum mechanics [with G. García-Calderón]. J. Phys. A: Math. Gen. 13, L185 (1980).

    Google Scholar 

  136. Review of the group theory behind the interacting boson model of the nucleus. In: Symmetries in Science, Ed. by B. Gruber and R.S. Millman (Plenum, 1980).

    Google Scholar 

  137. Group theory and nuclear models. Kinam 2, 79 (1980).

    Google Scholar 

  138. Group theory and the confrontation of nuclear collective models. In: Group Theoretical Methods in Physics. Cocoyoc, 1980. Ed. by K.B. Wolf (Springer-Verlag, Lecture Notes in Physics Vol. 135, 1980) pp. 382–398.

    Google Scholar 

  139. On the intrinsic shape of nuclei [with E. Chacón and S. Rubinstein]. In: Group Theoretical Methods in Physics. Cocoyoc, 1980. Ed. by K.B. Wolf, Springer-Verlag, Lecture Notes in Physics Vol. 135 (1980) pp. 382–398.

    Google Scholar 

  140. Confrontation of macroscopic and microscopic nuclear collective models [with E. Chacón and V. Vanagas]. J. Math. Phys. 22, 605 (1981).

    Google Scholar 

  141. On the structure of phase space [with T.H. Seligman]. J. Math. Phys. 22, 1338 (1981).

    Google Scholar 

  142. Is it possible to define an intrinsic quadrupole moment? Can it be measured? Does it imply a characteristic shape? Proceedings of the 4th Winter Meeting in Nuclear Physics (Oaxtepec, México 1981).

    Google Scholar 

  143. Canonical transformations relating the oscillator and Coulomb problems and their relevance for collective motions [with T.H. Seligman]. J. Math. Phys. 22, 1526 (1981).

    Google Scholar 

  144. Dynamical group, eigenstates and matrix elements for the collective Hamiltonian projected from a many body system [with E. Chacón]. Kinam 3, 3 (1981).

    Google Scholar 

  145. Confrontation of the confrontations of nuclear collective models [with O. Castaños, A. Frank, and P. Hess]. Phys. Rev. C24, 1367 (1981).

    Google Scholar 

  146. Group theory and collective degrees of freedom in many body systems. In: Proceedings of the II International Conference on Recent Progress in Many Body Theories (Springer-Verlag, 1981).

    Google Scholar 

  147. Canonical transformations and their representation in quantum mechanics. In: Group theory and its applications in physics. Proceedings of the 1980 Latin American School of Physics (American Institute of Physics Conference Proceedings, Vol. 71, 1981) pp.312–349.

    Google Scholar 

  148. Macroscopic and microscopic nuclear collective Hamiltonians. Their symmetry groups and the canonical transformation relating them. Proceedings of the 1981 Colloquium on Group Theoretical Methods in Physics. Physica 114A, 322 (1982).

    Google Scholar 

  149. Microscopic derivation of nuclear collective variables [with O. Castaños, E. Chacón, P. Hess, and A. Frank]. Phys. Rev. C25, 1611 (1982).

    Google Scholar 

  150. Complete set of states for microscopic nuclear collective models, [with O. Castaños, E. Chacón, A. Frank, and P. Hess]. J. Math. Phys. 23, 2537 (1982).

    Google Scholar 

  151. Unified approach to nuclear collective models Lecture Notes of the Granada School on the Interacting Boson Model (Springer-Verlag, 1982).

    Google Scholar 

  152. Does accidental degeneracy imply a symmetry group [with C. Quesne]. Ann. Phys. 148, 462 (1983).

    Google Scholar 

  153. Relativistic collective variables for many body systems [with P.O. Hess, W. Greiner, and G. Schmidt]. J. Phys. G: Nucl. Phys. 8, L179 (1982).

    Google Scholar 

  154. Accidental degeneracies and symmetry groups. Found. Phys. 13, 73 (1983).

    Google Scholar 

  155. SU(3) and SU(5) dynamical symmetries in the extended interacting boson model [with Sun Hong-Zhou, A. Frank, and P. van Isacker]. Kinam, 5, 135 (1983).

    Google Scholar 

  156. A hidden symmetry in collective excitations of many body systems [with O. Castaños and A. Frank]. Group Theoretical Methods in Physics Proceedings, Istanbul, Turkey, 1983. Springer-Verlag, Lecture Notes in Physics Vol. 180, (1983).

    Google Scholar 

  157. Collectivity and Geometry. I. General Approach. J. Math. Phys. 25, 1555 (1984).

    Google Scholar 

  158. Collectivity and Geometry. II. The two dimensional case [with E. Chacón and P. Hess]. J. Math. Phys. 25, 1565 (1984).

    Google Scholar 

  159. Collectivity and Geometry. III the three dimensional case in the Sp(6) ⊃ Sp(2) × O(3) chain for closed shells [with O. Castaños and E. Chacón]. J. Math. Phys. 25, 2815 (1984).

    Google Scholar 

  160. Geometry of Nuclear Collective Motions. Proceedings of Group Theoretical Methods in Physics, Trieste, 1983. Springer-Verlag, Lecture Notes in Physics Vol. 201 (1984).

    Google Scholar 

  161. Analytic expressions for the matrix elements of the generators of Sp(6) in the Sp(6) ⊃ U(3) basis [with O. Castaños and E. Chacón]. J. Math. Phys. 25, 1211 (1984).

    Google Scholar 

  162. Accidental degeneracies in the Zeeman effect and the symmetry groups [with N. Méndez, E. Murow, and J.W.B. Hughes]. Ann. Phys. 155, 231 (1984).

    Google Scholar 

  163. Pseudoatoms and atoms in strong magnetic fields [with N. Méndez and E. Murow]. Ann. Phys. 163, 1 (1985).

    Google Scholar 

  164. Symmetry constrained bosons and collectivity. Nucl. Phys. A421, 81 (1984).

    Google Scholar 

  165. Constrained bosons for collective states in open shell nuclei [with E. Chacón and O. Castaños]. Proceedings of the XIII Colloquium on Group Theoretical Methods in Physics, University of Maryland (World Publishing Co., Singapore, 1984).

    Google Scholar 

  166. Boson realization of Sp(4) I. The matrix formulation [with O. Castaños, E. Chacón, and C. Quesne]. J. Math. Phys. 26, 2107 (1985).

    Google Scholar 

  167. Boson realization of symplectic algebras J. Phys. A: Math. Gen. 18, 21 (1985).

    Google Scholar 

  168. Are there boson degrees of freedom in collective shell model states? Proceedings of the Drexel Conference on Nuclear Shell Model Theory (World Publishing Co., Singapore, 1984).

    Google Scholar 

  169. Generating kernel for boson realization of symplectic algebras [with O. Castaños and P. Kramer]. J. Phys. A: Math. Gen. 18, L493 (1985).

    Google Scholar 

  170. Boson realization of sp(4, R) II. The generating kernel formulation [with O. Castaños and P. Kramer]. J. Math. Phys. 27, 924 (1986).

    Google Scholar 

  171. Accidental degeneracy and symmetry Lie algebras [with R. Dirl]. J. Phys. A: Math. Gen. 18, 2423 (1985).

    Google Scholar 

  172. Collectivity and Geometry. IV. Sp(6) ⊃ Sp(2) × O(3) basis states for open shells [with R.T. Sharp and M. Nicolescu]. J. Math. Phys. 26, 2995 (1985).

    Google Scholar 

  173. Canonical transformations to action and angle variables and their representation in quantum mechanics. IV. Periodic potentials [with J. Flores, G. López, and G. Monsiváis]. Ann. Phys. 172, 156 (1986).

    Google Scholar 

  174. Critical analysis of algebraic collective models. Proceedings of the Dubrovnik Conference on Nuclear Structure, Reactions and Symmetries (World Scientific Vol.2, 1986) pp. 981–986.

    Google Scholar 

  175. Structure of phase space and quantum mechanics. Proceedings of the Phase Space Conference, Maryland (World Scientific, 1986).

    Google Scholar 

  176. Matrix representation of the generators of symplectic algebras. I. The case of Sp(4,R) [with O. Castaños]. J. Phys. A: Math. Gen. 20, 513 (1987).

    Google Scholar 

  177. Matrix representation of the generators of symplectic algebras. II. The general case with explicit results for Sp(6,R) [with E. Chacón]. J. Phys. A: Math. Gen. 20 (1987).

    Google Scholar 

  178. Collectivity and Geometry. V. Spectra and shapes in the two dimensional case [with E. Chacón and P. Hess]. J. Math. Phys. 28, 2223 (1987).

    Google Scholar 

  179. Group theory of the symplectic nuclear model. Proceedings of the Nuclear Physics Conference (Oaxtepec, 1987).

    Google Scholar 

  180. Stability of deuterons in strong magnetic fields [with G. Loyola]. Mod. Phys. Lett. A (Singapore) 3, 3435 (1988).

    Google Scholar 

  181. Stability of nuclei in strong magnetic fields Proceedings of the Nuclear Physics Conference (Oaxtepec, 1988) p. 233.

    Google Scholar 

  182. Collectivity and geometry VI. Spectra and shapes in the three dimensional case [with E. Chacón and P. O. Hess]. J. Math. Phys. 30, 970 (1989).

    Google Scholar 

  183. Wigner distribution functions and the representation of non-bijective canonical transformations in quantum mechanics [with R. Dirl and P. Kasperkovitz]. J. Phys. A21, 1835 (1988).

    Google Scholar 

  184. Collectivity and geometry. In: Modern Developments in Nuclear Physics, Novosibirsk Conference on Contemporary Problems in Nuclear Structure Physics, 1987. Ed. by O.P. Sushkov (World Scientific, Singapore, 1988) p. 353.

    Google Scholar 

  185. The symplectic nuclear model. Proceedings of the Varna Conference on Group Theoretical Methods in Physics. Springer-Verlag, Lecture Notes in Physics Vol. 313 (1988) p. 414.

    Google Scholar 

  186. Las tres caras de la espectroscopía: atómica, nuclear y sub-nuclear [with A. Sánchez]. Rev. Mex. Fís. 34, 511 (1988).

    Google Scholar 

  187. Relativistic symplectic model for scalar-quark systems. Proceedings of the Conference on Space-Time Symmetries. Nucl. Phys. B (Proc. Suppl.) 6, 76 (1989).

    Google Scholar 

  188. Coherent states and accidental degeneracy for a charged particle in a magnetic field [with G. Loyola and A. Szczepaniak]. Am. J. Phys. 57, 811 (1989).

    Google Scholar 

  189. Accidental degeneracy and the structure of matter in strong magnetic fields [with G. Loyola and A. Szczepaniak]. In: Symmetry in Science III (Plenum Press, 1989) pp. 311–322.

    Google Scholar 

  190. The Dirac oscillator [with A. Szczepaniak]. J. Phys. A: Math Gen. 22, L817 (1989).

    Google Scholar 

  191. The two body Dirac oscillator [with G. Loyola and A. Szczepaniak]. Anniversary Volume in Honor of J.J. Giambiaggi (World Scientific, Singapore, 1990).

    Google Scholar 

  192. The Dirac oscillator and its contribution to the baryon mass formula [with G. Loyola, A. Szczepaniak, C. Villegas, and N. Aquino]. Proceedings of the Rio de Janeiro International Workshop on Relativistic Aspects of Nuclear Physics (World Scientific, Singapore, 1990) pp. 271–307.

    Google Scholar 

  193. Symmetry Lie algebra of the Dirac oscillator [with C. Quesne]. J. Phys. A: Math. Gen. 23, 2263 (1990).

    Google Scholar 

  194. Art or Science: The symmetry Lie algebra for a Hamiltonian with accidental degeneracy [with C. Quesne and G. Loyola]. Ann. Phys. 198, 103 (1990).

    Google Scholar 

  195. Relativistic mass formula for baryons [with G. Loyola and C. Villegas]. Proceedings of the XIII Oaxtepec Conference on Nuclear Physics (1990) pp. 187–196.

    Google Scholar 

  196. Anomalous basis for representations of the Poincaré Group [with G. Loyola and C. Villegas]. J. Math Phys. (1990).

    Google Scholar 

  197. Comparison between perturbative and exact transitions induced by an interaction [with G. Loyola, and C. Villegas]. Am. J. Phys. (1990).

    Google Scholar 

  198. Exact time dependent transitions to negative energy states, due to an interaction [with G. Loyola and C. Villegas]. Festschrift In Honor of the 70th birthday of Jayme Tiomno (World Scientific, 1990).

    Google Scholar 

  199. Dynamical model for heavy ion collisions with a single resonance [with G. Loyola and C. Villegas]. Phys. Rev. C. (1990).

    Google Scholar 

  200. Relativistic invariance of a many body system with a Dirac oscillator interaction [with G. Loyola and C. Villegas]. Proceedings of Moscow Colloquium on Group Theory and its Applications (Springer-Verlag, Lecture Notes in Physics Vol. 382, 1991.) pp. 339–345.

    Google Scholar 

  201. The decay process: an exactly soluble example and its implications [with G. García Calderón and G. Loyola]. These Proceedings.

    Google Scholar 

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Authors and Affiliations

  1. Instituto de Física and CUCC, UNAM, Mexico

    Jorge Flores

  2. Instituto de Ciencias Nucleases, UNAM, Mexico

    Alejandro Frank

  3. Instituto de Física, Laboratorio de Cuernavaca, UNAM, Mexico

    Thomas H. Seligman

Authors
  1. Jorge Flores
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  2. Alejandro Frank
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  3. Thomas H. Seligman
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Editors and Affiliations

  1. Instituto de Ciencias Nucleares, Universidad Nacional Autónoma de México, Apdo. Postal 20-543, 01000, México DF, Mexico

    Alejandro Frank

  2. Instituto de Investigaciones en Matemáticas Aplicadas y en Sistemas, Universidad Nacional Autónoma de México, Apdo. Postal 139-B, 62191, Cuernavaca, Morelos, México DF, Mexico

    Kurt Bernardo Wolf

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© 1992 Springer-Verlag Berlin Heidelberg

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Flores, J., Frank, A., Seligman, T.H. (1992). Group Theory and the Harmonic Oscillator: The Work of Marcos Moshinsky. In: Frank, A., Wolf, K.B. (eds) Symmetries in Physics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-77284-9_1

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  • DOI: https://doi.org/10.1007/978-3-642-77284-9_1

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