Abstract Formulation of the Quantum Mechanical Oscillator Phase Problem
- 1 June 1971
- journal article
- research article
- Published by AIP Publishing in Journal of Mathematical Physics
- Vol. 12 (6) , 1021-1026
- https://doi.org/10.1063/1.1665669
Abstract
The phase operators ``cosine'' and ``sine'' are characterized as a special and peculiar class of tridiagonal operators, defined on an abstract separable Hilbert space. The two disjoint sets of these operators, which lie on the unit sphere of the algebra of bounded operators, are convex and closed in the uniform topology. The whole treatment gives a new and systematic aspect to the quantum mechanical oscillator phase problem.Keywords
This publication has 9 references indexed in Scilit:
- Structure of the Point Spectrum of Schrödinger-Type Tridiagonal OperatorsJournal of Mathematical Physics, 1970
- Some Mathematical Properties of Oscillator Phase OperatorsJournal of Mathematical Physics, 1970
- Approximate point spectrum of a weighted shiftTransactions of the American Mathematical Society, 1970
- Angle and Phase Coordinates in Quantum MechanicsPhysical Review B, 1969
- Spectral Theory of the Difference Equation f(n + 1) + f(n − 1) = [E − φ(n)]f(n)Journal of Mathematical Physics, 1969
- Harmonic-oscillator phase operatorsIl Nuovo Cimento B (1971-1996), 1968
- Phase and Angle Variables in Quantum MechanicsReviews of Modern Physics, 1968
- Minimum Uncertainty Product, Number-Phase Uncertainty Product, and Coherent StatesJournal of Mathematical Physics, 1968
- Hyponormal operatorsPacific Journal of Mathematics, 1962