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

Abstract

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, py) 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.