Quantum operators in Weyl quantization procedure via Wigner representation of quantum mechanics - quantum phase operator as a special case
Abstract
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.
Source:
Fortschritte Der Physik-Progress of Physics, 2003, 51, 2-3, 195-197Publisher:
- Wiley-VCH Verlag
DOI: 10.1002/prop.200310025
ISSN: 0015-8208
WoS: 000181566900023
Scopus: 2-s2.0-0037232828
Collections
Institution/Community
GraFarTY - JOUR AU - Davidović, Milena PY - 2003 UR - https://grafar.grf.bg.ac.rs/handle/123456789/52 AB - 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. PB - Wiley-VCH Verlag T2 - Fortschritte Der Physik-Progress of Physics T1 - Quantum operators in Weyl quantization procedure via Wigner representation of quantum mechanics - quantum phase operator as a special case EP - 197 IS - 2-3 SP - 195 VL - 51 DO - 10.1002/prop.200310025 ER -
@article{ author = "Davidović, Milena", year = "2003", abstract = "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.", publisher = "Wiley-VCH Verlag", journal = "Fortschritte Der Physik-Progress of Physics", title = "Quantum operators in Weyl quantization procedure via Wigner representation of quantum mechanics - quantum phase operator as a special case", pages = "197-195", number = "2-3", volume = "51", doi = "10.1002/prop.200310025" }
Davidović, M.. (2003). Quantum operators in Weyl quantization procedure via Wigner representation of quantum mechanics - quantum phase operator as a special case. in Fortschritte Der Physik-Progress of Physics Wiley-VCH Verlag., 51(2-3), 195-197. https://doi.org/10.1002/prop.200310025
Davidović M. Quantum operators in Weyl quantization procedure via Wigner representation of quantum mechanics - quantum phase operator as a special case. in Fortschritte Der Physik-Progress of Physics. 2003;51(2-3):195-197. doi:10.1002/prop.200310025 .
Davidović, Milena, "Quantum operators in Weyl quantization procedure via Wigner representation of quantum mechanics - quantum phase operator as a special case" in Fortschritte Der Physik-Progress of Physics, 51, no. 2-3 (2003):195-197, https://doi.org/10.1002/prop.200310025 . .