کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
9867167 1529974 2005 18 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
On infinite walls in deformation quantization
موضوعات مرتبط
مهندسی و علوم پایه فیزیک و نجوم فیزیک و نجوم (عمومی)
پیش نمایش صفحه اول مقاله
On infinite walls in deformation quantization
چکیده انگلیسی
We examine the deformation quantization of a single particle moving in one dimension (i) in the presence of an infinite potential wall, (ii) confined by an infinite square well, and (iii) bound by a delta function potential energy. In deformation quantization, considered as an autonomous formulation of quantum mechanics, the Wigner function of stationary states must be found by solving the so-called ⋆-genvalue (“stargenvalue”) equation for the Hamiltonian. For the cases considered here, this pseudo-differential equation is difficult to solve directly, without an ad hoc modification of the potential. Here we treat the infinite wall as the limit of a solvable exponential potential. Before the limit is taken, the corresponding ⋆-genvalue equation involves the Wigner function at momenta translated by imaginary amounts. We show that it can be converted to a partial differential equation, however, with a well-defined limit. We demonstrate that the Wigner functions calculated from the standard Schrödinger wave functions satisfy the resulting new equation. Finally, we show how our results may be adapted to allow for the presence of another, non-singular part in the potential.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Annals of Physics - Volume 317, Issue 2, June 2005, Pages 474-491
نویسندگان
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