Two-dimensional oscillator in a magnetic field

The energy and eigenstate spectrum of a charged particle in the electric field of a 2D anisotropic oscillator and in a uniform magnetic field is considered. The exact analytic solution to the problem is obtained for an arbitrary magnetic field strength. The characteristic features of variation of the energy spectrum depending on the magnetic field strength are analyzed. The results of this study are of interest for the quantum-mechanical theory of magnetism and can be used to simulate the magnetic properties of atoms and molecules.