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In the present paper the author evaluates the path integral of a chargedanisotropic Harmonic Oscillator (HO) in crossed electric and magnetic fields bytwo alternative methods. Both methods enable a rather formal calculation andcircumvent some mathematical delicate issues such as the occurrence of aninfinite Normalization constant and ambiguities with path integral calculationswhen magnetic fields are present. The \emph{$1^{\text{st}}$} method usescomplex Fourier series and a regularization scheme via theRiemann-$\zeta$-function. The \emph{$2^{\text{nd}}$} method evaluates the pathintegral by transforming the Lagrangian to a uniformly rotating system. Thelatter method uses the fact that the Lorentz- and Coriolis force have the samefunctional form. Both forces cancel each other within the rotating system giventhat it rotates with Larmor frequency $\omega_{L}$. This fact simplifiesconsiderably the calculation of the path integral.

Feynman Path Integral of a charged anisotropic HO in crossed electric and magnetic fields. Alternative calculational methods