In this project, I have examined quantum dynamics of some systems from unique perspectives.  In particular, our recent proposal of how to construct solvable quantum models for time-dependent two-level systems has been applied to a few quantum systems to obtain new insights and results.

We have considered a quantum two-level system (spin 1/2 particle) under a time-dependent classical magnetic field (semi-classical Rabi system) and succeeded in extending the so-called resonance condition to more general one.

Our method is applied to a system of a pair of two-level systems interacting to each other under external time-dependent magnetic fields.  The total dynamics can be reduced to two independent two-dimensional subdynamics only if the total Hamiltonian is endowed with a symmetry.  A condition under which a complex quantum four-level system can be solved analytically has thus been clarified.

Our proposal is nothing but a new parametrization of a solution for time-dependent Hamiltonian systems.  This knowledge has enabled us to parametrize transition amplitudes between instantaneous eigenstates of time-dependent Hamiltonian for quantum two-level system.  The result has been utilized to evaluate the quantum adiabatic condition and we have clarified what was wrong with the traditional adiabatic condition and derived a correct adiabatic condition.