The Discussion Of The Cyclic States Existence Of Forced Oscillator And The Calculation Of The Nonadiabatic Berry Phase By Using The Coherent States

In the long period after the founded of Quantum mechanics in 1925, the physicalquantity that people were familiar with just related with the original states and finalstates. That is called state function. Though there was a kind of phase differencedepended with not only the original and final states but also the whole course of theevolution presented by Dirac in 1930, the geometric phase has been really recognizedafter the presentation of adiabatic geometric phase and nonadiabatic geometric in 80's.This kind geometric phase has revealed the entirety and the topological property ofthe Quantum mechanics. Now, many important effects are related with the geometricphase, such as the quantum Hall effect, atomic laser. In this paper, we introduced the concept and the property of the adiabatic geometricphase and non-adiabatic geometric phase. In the part of our work, we choose animportant kind of forced oscillator to be our subject investigated to discuss theproblems related with the non-adiabatic geometric phase. We know that thenon-adiabatic geometric phase is the result of the cyclic evolution;it is related with akind of special state which is called cyclic origin state. We will not get thenon-adiabatic geometric phase before we've find the cyclic origin states. But as far aspresent research status, there is no efficient method to find the cyclic states of onesystem. People only can find and construct the cyclic states by chances. So the mainpart of our research is the discussion of cyclic states of this kind forced oscillatorsystem. We use the coherent state to be the original state of the system, and find thatwhether the system has the cyclic states have been determined by the form of theforced term of the oscillator. If the forced term satisfies one condition, then the systemhas the cyclic original states. So, for this oscillator system, we find a criterion. Use thecriterion we can judge whether the system has the coherent form cyclic original statesor does not have any form cyclic original states. Our result could be used beforepeople calculate the non-adiabatic geometric phase, if the system doesn't satisfy ourcriterion, the work should not be continued. Thus, the criterion can be used lest theuseless work should be done.