Energy eigenvalues from an analytical transfer matrix method

doi:10.1088/1674-1056/19/4/040306

中国物理B ›› 2010, Vol. 19 ›› Issue (4): 40306-040306.doi: 10.1088/1674-1056/19/4/040306

Energy eigenvalues from an analytical transfer matrix method

何英, 张凡明, 杨艳芳, 李春芳

Department of Physics, Shanghai University, Shanghai 200444, China

收稿日期:2009-11-05 修回日期:2009-11-30 出版日期:2010-04-15 发布日期:2010-04-15
基金资助:
Project supported by the National Natural Science Foundation of China (Grant Nos.~60877055 and 60806041), the Shanghai Rising-Star Program, China (Grant No.~08QA14030), the Innovation Funds for Graduates of Shanghai University, China (Grant No. SHUCX09202

Energy eigenvalues from an analytical transfer matrix method

He Ying(何英)^†, Zhang Fan-Ming(张凡明), Yang Yan-Fang(杨艳芳), and Li Chun-Fang(李春芳)

Department of Physics, Shanghai University, Shanghai 200444, China

Received:2009-11-05 Revised:2009-11-30 Online:2010-04-15 Published:2010-04-15
Supported by:
Project supported by the National Natural Science Foundation of China (Grant Nos.~60877055 and 60806041), the Shanghai Rising-Star Program, China (Grant No.~08QA14030), the Innovation Funds for Graduates of Shanghai University, China (Grant No. SHUCX09202

摘要/Abstract

摘要： A detailed procedure based on an analytical transfer matrix method is presented to solve bound-state problems. The derivation is strict and complete. The energy eigenvalues for an arbitrary one-dimensional potential can be obtained by the method. The anharmonic oscillator potential and the rational potential are two important examples. Checked by numerical techniques, the results for the two potentials by the present method are proven to be exact and reliable.

Abstract: A detailed procedure based on an analytical transfer matrix method is presented to solve bound-state problems. The derivation is strict and complete. The energy eigenvalues for an arbitrary one-dimensional potential can be obtained by the method. The anharmonic oscillator potential and the rational potential are two important examples. Checked by numerical techniques, the results for the two potentials by the present method are proven to be exact and reliable.

Key words: analytical transfer matrix method, energy eigenvalues, bound state, one-dimensional potential

中图分类号: (Solutions of wave equations: bound states)

03.65.Ge

03.65.Fd (Algebraic methods) 02.10.Yn (Matrix theory) 02.10.Ud (Linear algebra)

何英, 张凡明, 杨艳芳, 李春芳. Energy eigenvalues from an analytical transfer matrix method[J]. 中国物理B, 2010, 19(4): 40306-040306.

He Ying(何英), Zhang Fan-Ming(张凡明), Yang Yan-Fang(杨艳芳), and Li Chun-Fang(李春芳). Energy eigenvalues from an analytical transfer matrix method[J]. Chin. Phys. B, 2010, 19(4): 40306-040306.

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Energy eigenvalues from an analytical transfer matrix method

Energy eigenvalues from an analytical transfer matrix method

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