The Weyl-Wigner-Moyal formalism on a discrete phase space. I. A Wigner function for a nonrelativistic particle with spin
| Autor: | Maciej Przanowski, Francisco J. Turrubiates, Jaromir Tosiek |
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| Rok vydání: | 2018 |
| Předmět: |
Physics
Quantum Physics 0303 health sciences Quantum particle 030302 biochemistry & molecular biology Hilbert space General Physics and Astronomy FOS: Physical sciences Landau quantization 03 medical and health sciences symbols.namesake Formalism (philosophy of mathematics) Star product Phase space symbols Bijection Wigner distribution function Quantum Physics (quant-ph) 030304 developmental biology Mathematical physics |
| DOI: | 10.48550/arxiv.1812.07325 |
| Popis: | The Weyl-Wigner-Moyal formalism for quantum particle with discrete internal degrees of freedom is developed. A one to one correspondence between operators in the Hilbert space $L^{2}(\mathbb{R}^{3})\otimes{\mathcal{H}}^{(s+1)}$ and functions on the phase space $\mathbb{R}^{3}\times\mathbb{R}^{3}\times \{0,...,s\} \times\{0,...,s\}$ is found. The expressions for the Stratonovich-Weyl quantizer, star product and Wigner functions of such systems for arbitrary values of spin are obtained in detail. As examples the Landau levels and the corresponding Wigner functions for a spin $\frac{1}{2}$ nonrelativistic particle as well as the magnetic resonance for a spin $\frac{1}{2}$ nonrelativistic uncharged particle are analysed. Comment: 34 pages. New references have been added. Some comments have been included. The title has been modified |
| Databáze: | OpenAIRE |
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