Journal
EUROPEAN JOURNAL OF PHYSICS
Volume 39, Issue 2, Pages -Publisher
IOP PUBLISHING LTD
DOI: 10.1088/1361-6404/aa9ca5
Keywords
phase space; quantum harmonic oscillator; classical mechanics
Funding
- NSERC Discovery Grant
- National Science Foundation CAREER program [1455357]
- University of California Office of the President's Research Catalyst Award [CA-16-377655]
- US Office of Naval Research [N00014-17-1-2256]
- Direct For Mathematical & Physical Scien
- Division Of Physics [1455357] Funding Source: National Science Foundation
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In quantum mechanics, the operator representing the displacement of a system in position or momentum is always accompanied by a path-dependent phase factor. In particular, two non-parallel displacements in phase space do not compose together in a simple way, and the order of these displacements leads to different displacement composition phase factors. These phase factors are often attributed to the nonzero commutator between quantum position and momentum operators, but such a mathematical explanation might be unsatisfactory to students who are after more physical insight. We present a couple of simple demonstrations, using classical wave mechanics and classical particle mechanics, that provide some physical intuition for the phase associated with displacement operators.
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