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Singular perturbations of discrete spectrum

  • Elementary Particle Physics and Field Theory
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Abstract

Even solutions of the Schrödinger equation with retaining potential x2 are constructed for singular perturbation potentials λ|x|−ν. It is shown that the perturbation automatically entails an induced point potential, taking account of which the perturbation matrix elements and Rayleigh-Schrödinger series may be constructed when 1 < ν < 3/2. In the opposite case (3/2 ≤ν ≤2), although the solutions are analytic with respect to λ, not even diverging series can be obtained for the energy solutions without solution of the Schrödinger equation. The analogy with quantum field theory is explored.

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Author information

Authors and Affiliations

  1. M. V. Lomonosov Moscow State University, USSR

    V. B. Gostev, V. S. Mineev & A. R. Frenkin

Authors
  1. V. B. Gostev
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  2. V. S. Mineev
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  3. A. R. Frenkin
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Additional information

Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 3, pp. 58–64, March, 1988.

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Gostev, V.B., Mineev, V.S. & Frenkin, A.R. Singular perturbations of discrete spectrum. Soviet Physics Journal 31, 223–227 (1988). https://doi.org/10.1007/BF00898228

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  • DOI: https://doi.org/10.1007/BF00898228

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