Study On The Strict Solution Of Multi-dimensional Coupled And Forced Time-dependent Quantum Harmonic Oscillator And Quantum Phase

With the development of technology and quantum mechanics, scientists were doing experiments(such as particle motion in Paul Wells [1-4], plasmon resonance [5], the spin-containing particles in a magnetic field of sport [6], etc.), It found that the hamilton of these experimental systems is very similar to Time-dependent Dimensional Coupled and Forced Quantum Harmonic Oscillator Systems. Because of this, people contained more interesting in the study with Multidimensional Coupled and Forced Quantum Oscillator Subsystem. Meanwhile, the content is one of the few systems in quantum systems can use time-dependent Schrodinger wave equation solved exactly, and this Multi-dimensional Coupled and Forced Quantum Oscillator Subsystem containing the time evolution of the process of multi-dimensional coupled and forced quantum oscillator Subsystem analysis and quantum coherent state light field state vector and various properties of geometric phase is closely linked. In this paper, to solve the rigorous solution containing multidimensional when coupled quantum harmonic oscillator systems and forced-containing multi-mode Bose quadratic polynomial system and apply the theoretical knowledge requirements phase quantum phase by using generalized linear quantum transformation theory and mathematical operations, then solving the results were analyzed using the theory to explain the results and conclusions obtained with the corresponding academic significance for future researchers.The main contents of this thesis are about two aspects:1. The use of Generalized Linear Quantum Transformation Theory and Universal Mathematical approach gives a Multi-dimensional Coupled and Forced Quantum Oscillator Subsystem Time- evolution Operator obtained a rigorous solution and three forms of change evolution operator, and for its quantum phase. The results show that: for when the content is multi-dimensional coupled and forced quantum harmonic oscillator systems, non-adiabatic quantum phase non-handed case is PM type phase under non-adiabatic, handed the case of quantum phase is the phase of A-A in adiabatic conditions PM-type or A-A type geometric phase is approximately Berry phase. Then forced a one-dimensional quantum oscillator subsystem containing, for example, by solving the evolution operator and rigorous solution and quantum phase, to be operational to meet the above conclusions, to verify the correctness of the conclusion.2. The use of Generalized Linear Quantum Transformation Theory and Universal Mathematical Method to calculate the time-dependent evolution operator is given a multi-mode Bose quadratic polynomial system, and then given a rigorous solution of the system by the evolution operator, and apply the theory of phase knowledge seeking the quantum phase. The results show that: when n containing a non-adiabatic mode Bose quadratic polynomial system, non-handed geometric phase is universal, for when the system through the back-containing non-adiabatic geometric phase non-handed and A-A with both the same, for adiabatic system nonadiabatic Berry phase, a non-circulating back to the geometric phase approximation. Then-containing single-mode Bose quadratic polynomial system, for example, the conclusion was verified.Finally, I summarized my paper thesis.