We do not make the rotating-wave and markovian approximations on the interaction Hamiltonian and treat the environment as a non-markovian reservoir to the oscillators.

In the two-sublattice model, the Heisenberg exchange interaction Hamiltonian of the simple ferrimagnetic crystal can be made diagonalization by the use of HP, Fourier and Bogoliubov transformation.

The Hamiltonian solution of two-level atoms interaction with sounding lightwave field is given by using a new method of LLP transformation in solid state physics.