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On the stationary perturbation theory in quantum mechanics

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A simple method is proposed for solving the Shcrödinger equation in the presence of a perturbation. Formally exact expressions are obtained in the form of infinite series for the energies and wave functions without assuming that the perturbation is small. Under the additional assumption that it is small (in accordance with a well-defined criterion of smallness) the obtained results yield directly the results of Schrödinger's perturbation theory. The developed approach contains in compact form various formulations of perturbation theory. The calculations use neither the complex technique of projection operators nor the complicated formalism of Green's functions.

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Literature cited

  1. 1.

    L. D. Landau and E. M. Lifshitz, Quantum Mechanics: Non-Relativistic Theory, 3rd ed., Pergamon Press, Oxford (1977).

  2. 2.

    N. F. Mott and I. N. Sneddon, Wave Mechanics, Dover (1948).

  3. 3.

    K. Kumar, Perturbation Theory and the Nuclear Many Body Problem, Amsterdam (1965).

  4. 4.

    N. H. March, W. H. Young, and S. Sampanther, The Many-Body Problem in Quantum Mechanics, CUP, Cambridge (1967).

  5. 5.

    E. Schrödinger, Ann. Phys. (Leipzig),80, 437 (1926).

  6. 6.

    E. Wigner, Math. u. Naturw. Anz. der. Ungar. Acad. d. Wiss.,53, 477 (1935).

  7. 7.

    L. J. Brtllouin, Phys. Rad.,4, 1 (1933).

  8. 8.

    J. E. Lennard-Jones, Proc. R. Soc. London Ser. A,129, 604 (1930).

  9. 9.

    W. Riesenfeld and K. M. Watson, Phys. Rev.,104, 492 (1956).

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Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 11, pp. 33–36, November, 1980.

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Sabirov, R.K. On the stationary perturbation theory in quantum mechanics. Soviet Physics Journal 23, 939–942 (1980). https://doi.org/10.1007/BF00896163

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  • Wave Function
  • Quantum Mechanic
  • Perturbation Theory
  • Additional Assumption
  • Projection Operator