Semiclassical expansion of Wigner functions

We show that the time evolved Wigner function of a quantum particle under the action of a smooth potential can be formally expanded in powers of ℏ , where each term of the expansion can be computed in terms of the corresponding classical flow. Moreover the solution can be approximated by the N -orde...

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Veröffentlicht in:	Journal of mathematical physics 2006-05, Vol.47 (5), p.052103-052103-12
1. Verfasser:	Pulvirenti, M.
Format:	Artikel
Sprache:	eng
Schlagworte:	CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS ERRORS Exact sciences and technology EXPANSION Mathematical functions Mathematical methods in physics MATHEMATICAL SOLUTIONS Mathematics Physics POTENTIALS Quantum theory SCHROEDINGER EQUATION Sciences and techniques of general use SEMICLASSICAL APPROXIMATION WIGNER DISTRIBUTION
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Zusammenfassung:	We show that the time evolved Wigner function of a quantum particle under the action of a smooth potential can be formally expanded in powers of ℏ , where each term of the expansion can be computed in terms of the corresponding classical flow. Moreover the solution can be approximated by the N -order truncation with an error O ( ℏ N + 1 ) .
ISSN:	0022-2488 1089-7658
DOI:	10.1063/1.2200143