Soviet Physics Journal

, Volume 32, Issue 6, pp 421–424 | Cite as

Weakly singular perturbations of a discrete spectrum

  • V. B. Gostev
  • A. R. Frenkin
Elementary Particle Physics and Field Theory


We consider weakly singular perturbations λ¦x¦ν(0<ν<2) of an even restoring potential. We compute the matrix elements of the perturbation together with the additional point potential associated with the perturbation. It is shown that even for unperturbed wave functions, the matrix elements exist when 0 < ν < 3/2. The series for the Rayleigh-Schrödinger coefficients converge in all orders for the same interval in ν, regardless of the form of the restoring potential. For odd states, the matrix elements of the perturbation exist when 0 < ν < 3, while estimates for the Rayleigh-Schrödinger coefficients give the boundary ν = 2.


Wave Function Matrix Element Singular Perturbation Discrete Spectrum Additional Point 
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Copyright information

© Plenum Publishing Corporation 1989

Authors and Affiliations

  • V. B. Gostev
    • 1
  • A. R. Frenkin
    • 1
  1. 1.M. V. Lomonosov Moscow State UniversityUSSR

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