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