Use of operator wave functions to construct a refined correspondence principle via the quantum mechanics of Wigner and Moyal

Use of operator wave functions to construct a refined correspondence principle via the quantum mechanics of Wigner and Moyal

We represent the momentum operator p by p+(h//2i)(∂/∂p) and the position operator q by q−(h//2i)(∂/∂p). We then apply each resulting operator that appears in the nonrelativistic quantum mechanics of Schrödinger and Heisenberg to the constant 1. What results is a Wigner–Moyal theory which is as compl...

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Bibliographic Details
Published in:American journal of physics Vol. 48; no. 11; pp. 964 - 970
Main Author: Snygg, John
Format: Journal Article
Language:English
Published: 01-11-1980
Subjects:
LINEAR MOMENTUM
SCHROEDINGER EQUATION
HEISENBERG PICTURE
QUANTUM OPERATORS
CLASSICAL MECHANICS
WIGNER THEORY
CORRELATIONS
POSITION OPERATORS
QUANTUM MECHANICS
WAVE FUNCTIONS
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Summary:We represent the momentum operator p by p+(h//2i)(∂/∂p) and the position operator q by q−(h//2i)(∂/∂p). We then apply each resulting operator that appears in the nonrelativistic quantum mechanics of Schrödinger and Heisenberg to the constant 1. What results is a Wigner–Moyal theory which is as complete as the usual Schrödinger–Heisenberg theory. Replacing Planck’s constant h/ by zero in the Wigner–Moyal theory results in the classical physics of Newton. We thereby obtain a refined correspondence principle.
ISSN:0002-9505
1943-2909
DOI:10.1119/1.12197