Integration of the Schrodinger equation by canonical transformations

被引:10
|
作者
Tsaur, G [1 ]
Wang, JP [1 ]
机构
[1] Acad Sinica, Inst Atom & Mol Sci, Taipei 106, Taiwan
来源
PHYSICAL REVIEW A | 2002年 / 65卷 / 01期
关键词
D O I
10.1103/PhysRevA.65.012104
中图分类号
O43 [光学];
学科分类号
070207 ; 0803 ;
摘要
Owing to the operator nature of the quantum dynamical variables, classical canonical transformations for integrating the equations of motion cannot be extended to the quantum domain. In this paper, a general procedure is developed to construct the sequences of quantum canonical transformations for integrating the Schrodinger equations. The sequence is made of three elementary canonical transformations that constitute a much larger class than the unitary transformations. In conjunction with the procedure, we also developed a factorization technique that is analogous to the method of integration factor in classical integration. For demonstration, with the same procedure we integrate nine nontrivial models, including the centripetal barrier potential, the Kratzer's molecular potential, the Morse potential, the Poschl-Teller potential, the Hulthen potential, etc.
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页数:7
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