An eigenfunction expansion for the Schrodinger equation with arbitrary non-central potentials

TASELI H., Erhan I., Ugur O.

JOURNAL OF MATHEMATICAL CHEMISTRY, vol.32, no.4, pp.323-338, 2002 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 32 Issue: 4
  • Publication Date: 2002
  • Doi Number: 10.1023/a:1022949421571
  • Journal Name: JOURNAL OF MATHEMATICAL CHEMISTRY
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.323-338
  • Middle East Technical University Affiliated: Yes

Abstract

An eigenfunction expansion for the Schrodinger equation for a particle moving in an arbitrary non-central potential in the cylindrical polar coordinates is introduced, which reduces the partial differential equation to a system of coupled differential equations in the radial variable r. It is proved that such an orthogonal expansion of the wavefunction into the complete set of Chebyshev polynomials is uniformly convergent on any domain of (r, theta). As a benchmark application, the bound states calculations of the quartic oscillator show that both analytical and numerical implementations of the present method are quite satisfactory.