Schrödinger equations with power potentials

Jacek Karwowski*, Henryk A. Witek

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

1 Scopus citations

Abstract

General formulae for solutions of the Schrödinger equation with power potentials are derived. The wavefunctions are expressed as products of the asymptotic factors and special forms of the Hessenberg determinants, in general, of infinite order. Conditions under which the order of the determinants becomes finite are determined. It is shown that solutions represented by the finite-order determinants may exist only if the highest power of the radial variable in the potential function is even.

Original languageEnglish
Pages (from-to)932-940
Number of pages9
JournalMolecular Physics
Volume114
Issue number7-8
DOIs
StatePublished - 17 Apr 2016

Keywords

  • Hessenberg determinant
  • quasi-exactly solvable model
  • recurrence relation
  • Schrödinger equation

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