Study On The Wavefunction Of Time Dependent Anisotropic Coupled Harmonic Oscillator

Time-dependent harmonic oscillator is a very important physical model. it can beused to describe many physical systems, and it is very important in many fields, suchas the motion of ion in the Paul trap, atomic and molecular adsorption on the surfaceof solid and quantum field theory, quantum optics, mesoscopic physics, biophysicsfields and so on. As time-dependent harmonic oscillators are important in variousfields, people have done a lot of discussion it. The main methods to study it are LRinvariant theory, the unitary transformation method, test function. For the time-dependent anisotropic coupled harmonic oscillators, its analytic solution is verydifficult to calculate. In the case,it is often to use computer is solved by numericalmethod. As study on the analytic solution of this system is very rare, so getting thesolution of time-dependent anisotropy coupled oscillators in general solution issignificant. This thesis is mainly talking about getting the generalized form wavefunction of time-dependent anisotropic coupled harmonic oscillator system by LRinvariant method. The parameters of the wave function can be determined by solvinga series of differential equations when the specific the form of mass andfrequency.Thus we get the wave function of general time-dependent anisotropiccoupled oscillators.Using the wave function is obtained the quantum fluctuations ofcoordinate and momentum.