Quantum Action Angle Variables for Harmonic Oscillators

Newton, Roger G.

doi:10.1016/0003-4916(80)90213-4

Quantum Action Angle Variables for Harmonic Oscillators

Roger G. Newton
(
- Princeton, Inst. Advanced Study and
- Princeton U.
)

Mar, 1979

39 pages

Published in:

Annals Phys. 124 (1980) 327

DOI:

10.1016/0003-4916(80)90213-4

Report number:

Print-79-0406 (IAS,PRINCETON)

View in:

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Abstract: (Elsevier)

The well-known difficulties of defining a phase operator of an oscillator, caused by the lower bound on the number operator, is overcome by enlarging the physical Hilbert space by means of a spin-like, two-valued quantum number. On the enlarged space a phase representation exists on which trigonometric functions of the phase are numbers, and the “number of quanta” is a differential operator. Physical results are recovered by projection on the “upper components.” Coherent states, indeterminacy relations, as well as generalizations to other Hamiltonians, including the quantum analog of the quasi-periodic case, are discussed.

linear space
MODEL: OSCILLATOR
QUANTUM NUMBER
QUANTUM MECHANICS: COHERENT STATE
SPIN
QUANTUM MECHANICS: OPERATOR ALGEBRA
QUANTUM MECHANICS: COMMUTATION RELATIONS