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Hidden symmetries and thermodynamic properties for a harmonic oscillator plus an inverse square potential
Author(s) -
Dong ShiHai,
LozadaCassou M.,
Yu Jiang,
JiménezÁngeles Felipe,
Rivera A. L.
Publication year - 2007
Publication title -
international journal of quantum chemistry
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.484
H-Index - 105
eISSN - 1097-461X
pISSN - 0020-7608
DOI - 10.1002/qua.21103
Subject(s) - eigenfunction , harmonic oscillator , eigenvalues and eigenvectors , wave function , vibrational partition function , inverse , homogeneous space , partition function (quantum field theory) , quantum mechanics , quantum harmonic oscillator , quantum , mathematical physics , entropy (arrow of time) , square (algebra) , physics , mathematics , molecular vibration , hot band , molecule , geometry
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. © 2006 Wiley Periodicals, Inc. Int J Quantum Chem, 2007
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