Analytical Solutions of the Schrödinger Equation with Power Potentials

Jacek Karwowski*, Henryk A. Witek

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

2 Scopus citations


Conditions for the existence of polynomial solutions of the Schrödinger equation with potentials which are linear combinations of powers of r ranging from -2 to 2m, where m is a non-negative integer, are derived and explicit expressions for the coefficients are given. Potentials with m = 0, 1, 2 are discussed in detail.

Original languageEnglish
Pages (from-to)101-108
Number of pages8
JournalJournal of the Chinese Chemical Society
Issue number1
StatePublished - Jan 2016


  • Exact solubility
  • Hessenberg determinant
  • Heun equation
  • Power potentials
  • Quasi-exact solubility
  • Schrödinger equation

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