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Journal of Yunnan Normal University

Algebraicalsolution to the energy level and wave function of one-dimensional harmonic oscillator

W. J. Chang

Published Jan 1, 2001• 0 citations
OpenAlex

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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•Mar 7, 2013•1 citation
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A quantum state corresponds to a specific wave function. We adopt a new mathematical method [1] to improve Dirac's ladder operator method. A set of orthonormal wave functions will be used to associate the operator with the square matrix corresponding to it. These allow us to determine the matrix elements by using the operator relations without having to know the specific wave functions. As a result, we can get the direct results of matrix mechanics and wave mechanics on one-dimensional Harmonic oscillator and their descriptions will be also unified.