Canonical Transformations in Quantum Mechanics - INSPIRE

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Canonical Transformations in Quantum Mechanics

Arlen Anderson
(
- McGill U. and
- Imperial Coll., London and
- Santa Barbara, KITP
)

May 22, 1992

27 pages

Published in:

Annals Phys. 232 (1994) 292-331

e-Print:

hep-th/9305054 [hep-th],
hep-th/9205080 [hep-th]

DOI:

10.1006/aphy.1994.1055

Report number:

MCGILL-92-29-REV,
IMPERIAL-TP-92-93-31,
NSF-ITP-93-61

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Abstract:

Quantum canonical transformations are defined algebraically outside of a Hilbert space context. This generalizes the quantum canonical transformations of Weyl and Dirac to include non-unitary transformations. The importance of non-unitary transformations for constructing solutions of the Schr\"odinger equation is discussed. Three elementary canonical transformations are shown both to have quantum implementations as finite transformations and to generate, classically and infinitesimally, the full canonical algebra. A general canonical transformation can be realized quantum mechanically as a product of these transformations. Each transformation corresponds to a familiar tool used in solving differential equations, and the procedure of solving a differential equation is systematized by the use of the canonical transformations. Several examples are done to illustrate the use of the canonical transformations. [This is an extensively revised version of hep-th-9205080: the first third of the paper is new material; the notation has been simplified, and further discussion has been added to the remainder.]

Note:

27 pages, McGill 92-29 (revised version--several typos fixed in examples)

References(25)

Figures(0)

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