A fundamental quantum-mechanical problem on the phase of quantum harmonic oscillators, which has remained an enigma for more than sixty years since the first treatment by Dirac, is completely solved. Contrary to the common belief that no Hermitian phase operators can be found to describe the phase properties of a quantum harmonic oscillator, a well-defined Hermitian phase operator with an appropriate classical limit is constructed unambiguously. The approach is different in nature from those of many previous attempts which were more or less based on the idea of polar decomposition of the annihilation operator. The fundamental difference between the quantum phase and the classical phase in spite of their conceptual consistency is pointed out and explained. The eigenvalue spectrum and eigenstates of the phase operator are obtained. Some important properties of the phase operator and phase states are investigated. / The rest of this research is devoted to the studies of multimode Gaussian squeezed states of quantum harmonic oscillators. Multimode squeeze operators and rotation operators are defined such that they have extremely similar algebraic properties as those of their single-mode counterparts. It is shown that the introduction of N-mode squeeze operators provides a convenient set of parameters to describe squeezing in multimode Gaussian squeezed states. The disentangling, normal ordering, and some other properties of N-mode squeeze operators are investigated. It is also shown that the time-evolution operator for a general N-mode quadratic Hamiltonian can be conveniently expressed as an operator product containing an N-mode squeeze operator, an N-mode rotation operator, and an N-mode displacement operator. As an application of this result, the dynamics of N-mode harmonic oscillators with time-dependent normal coordinates and frequencies is investigated and formulated by the use of these N-mode unitary operators. A general expression for the time-dependent transition amplitudes between two arbitrary N-mode boson number states is obtained and explicit results are given for the case of sudden changes in normal coordinates and frequencies. / Source: Dissertation Abstracts International, Volume: 50-12, Section: B, page: 5703. / Major Professor: William Clifford Rhodes. / Thesis (Ph.D.)--The Florida State University, 1989.
| Identifer | oai:union.ndltd.org:fsu.edu/oai:fsu.digital.flvc.org:fsu_78134 |
| Contributors | Ma, Xin., Florida State University |
| Source Sets | Florida State University |
| Language | English |
| Detected Language | English |
| Type | Text |
| Format | 86 p. |
| Rights | On campus use only. |
| Relation | Dissertation Abstracts International |
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