Abstract Formulation of the Quantum Mechanical Oscillator Phase Problem
作者： Evangelos K. Ifantis
DOI: 10.1063/1.1665669
关键词: Operator algebra 、 Spectral theorem 、 Optical phase space 、 Operator norm 、 Pure mathematics 、 Mathematics 、 POVM 、 Creation and annihilation operators 、 Second quantization 、 Operator theory 、 Mathematical physics 、 Statistical and Nonlinear Physics
摘要: The phase operators ``cosine'' and ``sine'' are characterized as a special peculiar class of tridiagonal operators, defined on an abstract separable Hilbert space. two disjoint sets these which lie the unit sphere algebra bounded convex closed in uniform topology. whole treatment gives new systematic aspect to quantum mechanical oscillator problem.
harvard.edu
scitation.org
aip.org
sci-hub.se 参考文章(8)
P. CARRUTHERS, MICHAEL MARTIN NIETO, Phase and Angle Variables in Quantum Mechanics Reviews of Modern Physics. ,vol. 40, pp. 411- 440 ,(1968) , 10.1103/REVMODPHYS.40.411
Roman Jackiw, Minimum Uncertainty Product, Number‐Phase Uncertainty Product, and Coherent States Journal of Mathematical Physics. ,vol. 9, pp. 339- 346 ,(1968) , 10.1063/1.1664585
J. ZAK, Angle and Phase Coordinates in Quantum Mechanics Physical Review. ,vol. 187, pp. 1803- 1810 ,(1969) , 10.1103/PHYSREV.187.1803
E. C. Lerner, Harmonic-oscillator phase operators Il Nuovo Cimento B. ,vol. 56, pp. 183- 186 ,(1968) , 10.1007/BF02711966
Evangelos K. Ifantis, Structure of the Point Spectrum of Schrödinger‐Type Tridiagonal Operators Journal of Mathematical Physics. ,vol. 11, pp. 3138- 3144 ,(1970) , 10.1063/1.1665104
E. C. Lerner, H. W. Huang, G. E. Walters, Some Mathematical Properties of Oscillator Phase Operators Journal of Mathematical Physics. ,vol. 11, pp. 1679- 1684 ,(1970) , 10.1063/1.1665310
Platon C. Deliyannis, Evangelos K. Ifantis, Spectral Theory of the Difference Equation f(n + 1) + f(n − 1) = [E − φ(n)]f(n) Journal of Mathematical Physics. ,vol. 10, pp. 421- 425 ,(1969) , 10.1063/1.1664855
William C. Ridge, Approximate point spectrum of a weighted shift Transactions of the American Mathematical Society. ,vol. 147, pp. 349- 356 ,(1970) , 10.1090/S0002-9947-1970-0254635-5