Physics – Quantum Physics
Scientific paper
2005-07-31
Can. J. Phys.84:557-563, 2006
Physics
Quantum Physics
6 pages, 0 figures, submitted to Canadian Journal of Physics, special issue for the proceedings of Canada Theory 1 (6/05, UBC)
Scientific paper
10.1139/P06-017
In deformation quantization (a.k.a. the Wigner-Weyl-Moyal formulation of quantum mechanics), we consider a single quantum particle moving freely in one dimension, except for the presence of one infinite potential wall. Dias and Prata pointed out that, surprisingly, its stationary-state Wigner function does not obey the naive equation of motion, i.e. the naive stargenvalue (*-genvalue) equation. We review our recent work on this problem, that treats the infinite wall as the limit of a Liouville potential. Also included are some new results: (i) we show explicitly that the Wigner-Weyl transform of the usual density matrix is the physical solution, (ii) we prove that an effective-mass treatment of the problem is equivalent to the Liouville one, and (iii) we point out that self-adjointness of the operator Hamiltonian requires a boundary potential, but one different from that proposed by Dias and Prata.
Kryukov Sergei
Walton Mark A.
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