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

doi:10.1002/qua.21103

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 journal › Article › peer-review

100 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 language	English (US)
Pages (from-to)	366-371
Number of pages	6
Journal	International Journal of Quantum Chemistry
Volume	107
Issue number	2
DOIs	https://doi.org/10.1002/qua.21103
State	Published - Feb 2007
Externally published	Yes

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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10.1002/qua.21103

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abstract = "The exact solutions of a one-dimensional Schr{\"o}dinger 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.",

keywords = "Factorization method, Hidden symmetry, Ladder operators, Partition function",

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AU - Dong, Shi Hai

AU - Lozada-Cassou, M.

AU - Yu, Jiang

AU - Jiménez-Ángeles, Felipe

AU - Rivera, A. L.

PY - 2007/2

Y1 - 2007/2

N2 - 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.

AB - 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.

KW - Factorization method

KW - Hidden symmetry

KW - Ladder operators

KW - Partition function

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JO - International Journal of Quantum Chemistry

JF - International Journal of Quantum Chemistry

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

Abstract

Keywords

ASJC Scopus subject areas

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