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Quantum operators in Weyl quantization procedure via Wigner representation of quantum mechanics ‐ quantum phase operator as a special case
Author(s) -
Davidović M.
Publication year - 2003
Publication title -
fortschritte der physik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.469
H-Index - 71
eISSN - 1521-3978
pISSN - 0015-8208
DOI - 10.1002/prop.200310025
Subject(s) - method of quantum characteristics , wigner distribution function , quantization (signal processing) , operator (biology) , phase space , mathematics , quantum mechanics , geometric quantization , quantum , mathematical physics , quantum dynamics , quantum process , physics , canonical quantization , quantum gravity , algorithm , biochemistry , chemistry , repressor , transcription factor , gene
Coherent states, in Wigner representation of quantum mechanics which is classical in structure with Wigner function playing the role of classical phase space probability distribution, and standard quantum mechanical expression for average values of corresponding Weyl quantum operators, general expression for matrix elements of the operator corresponding to phase of the oscillator by Weyl procedure, are obtained in the | n 〉 basis. The general expression for matrix elements in the same basis of any other operator is also obtained. As the only mathematical technique necessary in the proposed procedure is a simple change of variables to polar coordinates in the corresponding integrals, this way to introduce Weyl phase operator, and some other operators in Weyl quantization, greatly simplifies necessary derivations and calculations.