Hidden symmetries and thermodynamic properties for a harmonic oscillator plus an inverse square potential

Shi Hai Dong*, M. Lozada-Cassou, Jiang Yu, Felipe Jiménez-Ángeles, A. L. Rivera

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

70 Scopus citations

Abstract

The exact solutions of a one-dimensional Schrödinger equation with a harmonic oscillator plus an inverse square potential are obtained. The ladder operators constructed directly from the normalized wavefunctions are found to satisfy a su(1, 1) algebra. Another hidden symmetry is used to explore the relations between the eigenvalues and eigenfunctions by substituting x → -ix. The vibrational partition function Z is calculated exactly to study thermodynamic functions such as the vibrational mean energy U, specific heat C, free energy F, and entropy S. It is both interesting and surprising to find that both vibrational specific heat C and entropy S are independent of the potential strength α.

Original languageEnglish (US)
Pages (from-to)366-371
Number of pages6
JournalInternational Journal of Quantum Chemistry
Volume107
Issue number2
DOIs
StatePublished - Feb 2007
Externally publishedYes

Keywords

  • Factorization method
  • Hidden symmetry
  • Ladder operators
  • Partition function

ASJC Scopus subject areas

  • Atomic and Molecular Physics, and Optics
  • Condensed Matter Physics
  • Physical and Theoretical Chemistry

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