Classical Aspects of Quantum Walls in One Dimension

Details Classical Aspects of Quantum Walls in One Dimension Classical Aspects of Quantum Walls in One Dimension

2001-11-09

arxiv.org/abs/quant-ph/0111057v2

Physical Review A 66 (2002) 052102 (10)

Physics

Quantum Physics

TeX, 21 pages, 4 figures. v2: some parts of the text improved, new and improved figures

Scientific paper

10.1103/PhysRevA.66.052102

We investigate the system of a particle moving on a half line x >= 0 under the general walls at x = 0 that are permitted quantum mechanically. These quantum walls, characterized by a parameter L, are shown to be realized as a limit of regularized potentials. We then study the classical aspects of the quantum walls, by seeking a classical counterpart which admits the same time delay in scattering with the quantum wall, and also by examining the WKB-exactness of the transition kernel based on the regularized potentials. It is shown that no classical counterpart exists for walls with L < 0, and that the WKB-exactness can hold only for L = 0 and L = infinity.

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