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Journal of Hubei Institute for Nationalities

ALGEBRAIC SOLUTION TO THE ENERGY LEVEL AND WAVE FUNCTION OF ONE-DIMENSIONAL HARMONIC OSCILLATOR

Changrong Wang

Published Jan 1, 2000• 0 citations
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Abstract

In the research of one-dimensional harmonic oscillaton as the object in Heisenberg's picture.We have got two kinds of solutions of its energy level and wave fanction by algebraic approach of using matrix mechanics and factorization method.

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Science China Mathematics•Jan 1, 1991•0 citations
The one-dimensional harmonic oscillator is one of the few models in quantum mechanics that can be solved analytically, and it is used to exam the theories and methods of quantum mechanics, possessing rich connotations. Using the Fourier transform and the generating function of Hermite polynomials, the transformation from the eigenfunction in the coordinate representation to that in the momentum representation for a one-dimensional harmonic oscillator has been achieved. The equivalence and connection between the two representations for describing a one-dimensional harmonic oscillator are verified. The eigenenergies and eigenfunctions of the one-dimensional harmonic oscillator in the coordinate representation and momentum representation are also obtained by using the algebraic solution method, respectively. The equivalence of the two representations is further discussed. The idea of psolving physical problems in higher dimensional spaceq is emphasized, which deepens students' understanding of quantum mechanics and stimulates their interest in learning.