Some Mathematical Properties of Oscillator Phase Operators
- 1 May 1970
- journal article
- research article
- Published by AIP Publishing in Journal of Mathematical Physics
- Vol. 11 (5) , 1679-1684
- https://doi.org/10.1063/1.1665310
Abstract
A general definition of ``cosine'' and ``sine'' operators, C and S, for harmonic oscillator phase is proposed and its consequences examined. An important feature of the spectral analysis is the ``chain sequence'' condition which ensures that C and S have unit norm. The (nonunitary) operator U = C + iS is shown to be an annihilation‐type operator whose spectral properties bear a remarkable analogy to those of the standard annihilation operator, although its spectrum fills the unit circle rather than the entire complex plane. Statistical properties of the eigenstates of U are discussed briefly.Keywords
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