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arXiv:1809.03844 · Physical Review A

Eigenstates of linear combinations of phase operators

C V Sukumar

Published Feb 1, 1993• 3 citations
arXivHTMLPDF

Abstract

The eigenstates of linear combinations of the Susskind and Glogower phase operators [Physics 1, 49 (1964)] for the harmonic oscillator are constructed. It is shown that such eigenstates are squeezed states.
DOI
10.1103/physreva.47.1554

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It is pointed out that, while Suskind and Glogower claim “The phase operator for an oscillator is shown not to exist.”, they actually showed absolute phase operator, which is physically meaningless, does not exist. It is also pointed out that, they showed countably infinitely many trigonometric relative (relative between two oscillators) phase states, which form complete basis and are, in a sense, best possible quantum “phase states”, exist. In addition, continuously infinitely many phase states are constructed at classical, that is, infinitely many quanta, limit. Similarly, relative time states and operator are constructed with two oscillators with different angular velocities.