In this paper we solve exactly the problem of the spectrum and Feynmanpropagator of a charged particle submitted to both an anharmonic oscillator inthe plane and a constant and homogeneous magnetic field of arbitrary strengthaligned with the perpendicular direction to the plane. As we shall see in thebeginning of the letter the Hamiltonian, being a quadratic form, is easilydiagonalizable and the Classical Action can be used to construct the exactFeynman Propagator using the Stationary Phase Approximation. The result isuseful for the treatment of quasi two dimensional samples in the field ofmagnetic effects in nano-structures and quantum optics. The presented solution,after minor extensions, can also be used for motion in three dimensions, and infact it has been used for years in such cases. Also it can be used as a goodexercise of a Feynman Path Integral that can be calculated easily with just thehelp of the Classical Action.
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