Eiegenvalue problem for Schrödinger's equation with repulsive potential

S. Matsumoto, K. Kakazu, T. Nagamine

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1 Citation (Scopus)


Schrödinger's operator - (ℏ/2m)[d2/dr2 + (2/r)d/dr] + V(r) is studied, and what happens when V(r) approaches - ∞ rapidly as r→∞ is shown. The cases in which V(r)∼ - βr δ (β>0, δ > 2) as r→∞are covered. If V(r) approaches - ∞ rapidly, then the above operator is not self-adjoint and in order to get a self-adjoint operator a boundary condition must be imposed. For such a self-adjoint operator there are states that belong to the discrete energy spectrum. To obtain the discrete energy spectrum, a quantization rule that corresponds to the quantization rule of Bohr and Sommerfeld in old quantum mechanics is considered.

Original languageEnglish
Pages (from-to)232-237
Number of pages6
JournalJournal of Mathematical Physics
Issue number1
Publication statusPublished - 1986
Externally publishedYes

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics


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