Wigner functions of s waves

Jens Peder Dahl; S. Varro; A. Wolf; W. P. Schleich

doi:10.1103/PhysRevA.75.052107

Wigner functions of s waves

Jens Peder Dahl, S. Varro, A. Wolf, W. P. Schleich

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Abstract

We derive explicit expressions for the Wigner function of wave functions in D dimensions which depend on the hyperradius-that is, of s waves. They are based either on the position or the momentum representation of the s wave. The corresponding Wigner function depends on three variables: the absolute value of the D-dimensional position and momentum vectors and the angle between them. We illustrate these expressions by calculating and discussing the Wigner functions of an elementary s wave and the energy eigenfunction of a free particle.

Original language	English
Journal	Physical Review A
Volume	75
Issue number	5
Pages (from-to)	052107
ISSN	2469-9926
DOIs	https://doi.org/10.1103/PhysRevA.75.052107
Publication status	Published - 2007

Bibliographical note

Keywords

PHASE-SPACE FUNCTION
QUANTUM-MECHANICS
HYDROGEN-ATOM

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http://link.aps.org/doi/10.1103/PhysRevA.75.052107

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abstract = "We derive explicit expressions for the Wigner function of wave functions in D dimensions which depend on the hyperradius-that is, of s waves. They are based either on the position or the momentum representation of the s wave. The corresponding Wigner function depends on three variables: the absolute value of the D-dimensional position and momentum vectors and the angle between them. We illustrate these expressions by calculating and discussing the Wigner functions of an elementary s wave and the energy eigenfunction of a free particle.",

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AU - Dahl, Jens Peder

AU - Varro, S.

AU - Wolf, A.

AU - Schleich, W. P.

PY - 2007

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N2 - We derive explicit expressions for the Wigner function of wave functions in D dimensions which depend on the hyperradius-that is, of s waves. They are based either on the position or the momentum representation of the s wave. The corresponding Wigner function depends on three variables: the absolute value of the D-dimensional position and momentum vectors and the angle between them. We illustrate these expressions by calculating and discussing the Wigner functions of an elementary s wave and the energy eigenfunction of a free particle.

AB - We derive explicit expressions for the Wigner function of wave functions in D dimensions which depend on the hyperradius-that is, of s waves. They are based either on the position or the momentum representation of the s wave. The corresponding Wigner function depends on three variables: the absolute value of the D-dimensional position and momentum vectors and the angle between them. We illustrate these expressions by calculating and discussing the Wigner functions of an elementary s wave and the energy eigenfunction of a free particle.

KW - PHASE-SPACE FUNCTION

KW - QUANTUM-MECHANICS

KW - HYDROGEN-ATOM

U2 - 10.1103/PhysRevA.75.052107

DO - 10.1103/PhysRevA.75.052107

M3 - Journal article

SN - 2469-9926

VL - 75

SP - 052107

JO - Physical Review A

JF - Physical Review A

IS - 5

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Wigner functions of s waves

Abstract

Bibliographical note

Keywords

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