New forms of wavefunctions for the isotropic harmonic oscillator in a time-dependent magnetic field

After a unitary transformation, exact wavefunctions of the time-dependent two-dimensional harmonic oscillator in a time-dependent magnetic field are written in the form of the product of two one-dimensional time-dependent harmonic oscillators in the ( x, p(y)) representation. Applying the Heisenberg correspondence principle (HCP) to the system, the exact classical solution is obtained from the quantum matrix elements. Meanwhile, the coherent state is discussed.