An algebraic approach to energy eigenvalue of anisotropicn-dimensional coupling harmonic oscillators

Abstract

Abstract:

The study of the Coupled harmonic oscillator is an important problem in quantum optics, because many actual physical problems are dependent on the model of the coupled harmonic oscillator , so studying the easy way to solve the coupled harmonic oscillator appears to be necessary. Through structuring a formal matrix by quadratic orthogonal mathematical theory and letting the Hamilton diagonalization of the n-dimensional anisotropic harmonic oscillators both coordinate and momentum coupling, this obtains its eigenvalue . And applying this method to solve the energy eigenvalue of three-dimensional coupling harmonic oscillator, this verifyied the correctness of the method at the same time. Since the method does not need to derive the concrete form of the transformation matrix, making it simple and easy to calculate the results to the eigenvalue problems of the Hamilton with symmetrical form. This algebraic methods is more universal and more effective.

Key words: quantum optics, coupling harmonic oscillators, quadratic orthogonal mathematical theory, energy eigenvalue, diagonalization

CLC Number:

O413.1

ZHANG Zhong, ZHOU Bo, WANG Pei-Ji, Tao-Ye-Wei. An algebraic approach to energy eigenvalue of anisotropicn-dimensional coupling harmonic oscillators[J]. J4, 2009, 26(4): 405-412.

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