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Acta Physica Sinica

Exact solution of a kind of n-dimensions non-spherical harmonic oscillator p otential

Long Chao-Yun, Ming-Lun Chen, Cai Shao-Hong, (1)贵州大学物理系,贵阳 550025; (2)贵州师范大学物理系，贵阳 550002

Published Jan 1, 2003• 1 citation
Publisher

Abstract

In this paper,the Schrdinger equation with a non-spherical harmonic oscillator potential in n-dimensions is solved.The exact energy equation and the normalized wave function are obtained.The general formulas of matrix elements of op erator rs are presented.
DOI
10.7498/aps.52.1858

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We present exact solutions of the Schrödinger equation with a harmonic oscillator plus an inverse squared potential in arbitrary dimensions. The ladder operators for the radial wavefunctions are established by the factorization method. We find that those operators together with satisfy the commutation relation of the generators of an su(1, 1) algebra. Some comments are made on the general calculation formula for off-diagonal matrix elements and the recurrence relation among them. Also, we show that this anharmonic oscillator possesses a hidden symmetry between E ( r ) and E (i r ) by substituting r → i r .