The Hamiltonian for two interacting particles is, as known
$$\hat H = - \frac{{{\hbar ^2}}}{{2{m_1}}}{\Delta _1} - \frac{{{\hbar ^2}}}{{2{m_2}}}{\Delta _2} + V({\vec r_1},{\text{ }}{\vec r_2}),$$
$${\Delta _1} \equiv \nabla _1^2 = \frac{{{\partial ^2}}}{{\partial x_1^2}} + \frac{{{\partial ^2}}}{{\partial y_1^2}} + \frac{{{\partial ^2}}}{{\partial z_1^2}}$$
and Δ2 is analogously defined. In a closed system the potential energy V depends only on the relative position of the particles, so we may write
$$\hat H = - \frac{{{\hbar ^2}}}{{2{m_1}}}{\Delta _1} - \frac{{{\hbar ^2}}}{{2{m_2}}}{\Delta _2} + V({\vec r_1} - {\vec r_2}).$$


Wave Function Coupling Term Electronic Wave Function Schrodinger Equation Free Atom 
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  1. 1.
    E. Fermi, Notes on Quantum Mechanics, University of Chicago Press, 1960.Google Scholar
  2. 2.
    N. Mott and I. Sneddon, Wave Mechanics and its Applications. Clarendon Press, Oxford 1948.Google Scholar
  3. 3.
    L.D. Landau and I. M. Lifshitz, Kvantovaya Mekhanika, Nauka, Moscow 1974.Google Scholar
  4. 4.
    P.R. Bunker and P. Jensen, Molecular Symmetry and Spectroscopy, NRC Research Press, Ottawa 1998.Google Scholar
  5. 5.
    L. Zülicke, Quantenchemie, Deutcher Verlag der Wissenschaften, Berlin 1973.Google Scholar
  6. 6.
    B.T. Suttcliffe F undamentals in Computational Quantum Chemistry, in Computational Techniques in Quantum Chemistry and Molecular Physics, (ed. G.H.F. Dierksen, B.T. Suttcliffe and A. Veillard) Reidel, Dordrecht 1974.Google Scholar
  7. 7.
    H.A. Bethe, Intermediate Quantum Mechanics, Benjamin, New York 1964.Google Scholar
  8. 8.
    J.C. Slater, Quantum Theory of Molecules and Solids vol. 1. Electronic Structure of Molecules, McGraw-Hill, New York 1963.Google Scholar
  9. 9.
    M. Born and W. Heisenberg, Ann. Phys. 84, 1 (1924)CrossRefGoogle Scholar
  10. 10.
    M. Born and J.R. Oppenheimer, Ann. Phys. 84, 457 (1927)CrossRefGoogle Scholar
  11. 11.
    M. Born and K. Huang, Dynamical Theory of Crystal Lattices, Oxford University Press, London 1954, Appendix VIII.Google Scholar
  12. 12.
    T. Azumi and K. Matsuzaki, Photochem. Photobiol., 25, 315 (1977)CrossRefGoogle Scholar
  13. 13.
    M. Baer, Physics Reports, 358, 75 (2002)CrossRefGoogle Scholar
  14. 14.
    H.J. Monkhorst, Phys. Rev. A36, 1544 (1987)CrossRefGoogle Scholar

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© Springer Science+Business Media New York 2003

Authors and Affiliations

  • István Mayer
    • 1
  1. 1.Chemical Research CenterHungarian Academy of SciencesBudapestHungary

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