  In the present paper the author evaluates the path integral of a charged
anisotropic Harmonic Oscillator (HO) in crossed electric and magnetic fields by
two alternative methods. Both methods enable a rather formal calculation and
circumvent some mathematical delicate issues such as the occurrence of an
infinite Normalization constant and ambiguities with path integral calculations
when magnetic fields are present. The \emph{$1^{\text{st}}$} method uses
complex Fourier series and a regularization scheme via the
Riemann-$\zeta$-function. The \emph{$2^{\text{nd}}$} method evaluates the path
integral by transforming the Lagrangian to a uniformly rotating system. The
latter method uses the fact that the Lorentz- and Coriolis force have the same
functional form. Both forces cancel each other within the rotating system given
that it rotates with Larmor frequency $\omega_{L}$. This fact simplifies
considerably the calculation of the path integral.
