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Cited by 552

The DOI matches its Crossref record; 45 of the 45 references it cites were found in a registry or an index.

Calculus for Functions of Noncommuting Operators and General Phase-Space Methods in Quantum Mechanics. I. Mapping Theorems and Ordering of Functions of Noncommuting Operators

Agarwal, G. S., Wolf, E.·1970·Physical Review D
DOI 10.1103/physrevd.2.2161
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Abstract

A new calculus for functions of noncommuting operators is developed, based on the notion of mapping of functions of operators onto $c$-number functions. The class of linear mappings, each member of which is characterized by an entire analytic function of two complex variables, is studied in detail. Closed-form solutions for such mappings and for the inverse mappings are obtained and various properties of these mappings are studied. It is shown that the most commonly occurring rules of association between operators and $c$-numbers (the Weyl, the normal, the antinormal, the standard, and the antistandard rules) belong to this class and are, in fact, the simplest ones in a clearly defined sense. It is shown further that the problem of expressing an operator in an ordered form according to some prescribed rule is equivalent to an appropriate mapping of the operator on a $c$-number space. The theory provides a systematic technique for the solution of numerous quantum-mechanical problems that were treated in the past by ad hoc methods, and it furnishes a new approach to many others. This is illustrated by a number of examples relating to mappings and ordering of operators.

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Metadata

Authors
Agarwal, G. S., & Wolf, E.
Venue
Physical Review D
Publisher
American Physical Society (APS)
Published
1970-11-15
Volume
2
Issue
10
Pages
2161-2186
ISSN
0556-2821 (ISSN-L)
DOI
10.1103/physrevd.2.2161
OpenAlex
W2176426498
Cited by
552
References
45
FWCI
2.77
Type
journal article
Language
en
Open access
closed

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