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Science China Physics Mechanics and Astronomy

New fundamental quantum mechanical operator-ordering identities for the coordinate and momentum operators

Hong-Yi Fan

Published Mar 25, 2012• 19 citations
Publisher
DOI
10.1007/s11433-012-4699-4

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In this paper, we introduce a new way to obtain the Q — P (P — Q) ordering of quantum mechanical operators, i.e., from the classical correspondence of Q — P (P — Q) ordered operators by replacing q and p with coordinate and momentum operators, respectively. Some operator identities are derived concisely. As for its applications, the single (two-) mode squeezed operators and Fresnel operator are examined. It is shown that the classical correspondence of Fresnel operator's Q — P (P — Q) ordering is just the integration kernel of Fresnel transformation. In addition, a new photo-counting formula is constructed by the Q — P ordering of operators.