Wave functions of a time-dependent harmonic oscillator in a static magnetic field

In this paper, we solve for the exact wave functions of a two-dimensional harmonic oscillator under the influence of a static magnetic field. This is done through the use of the so-called Ermakov invariants, similarity transformed so as to obtain a time-independent Schrodinger equation. In the same manner, time-dependent eigenvalues are also computed. It is shown that previous results for the invariants are particular cases for the ones found in this work.