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arXiv · 1901.05677

On the Feynman path integral for the magnetic Schroedinger equation with a polynomially growing electromagnetic potential

Wataru Ichinose
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Abstract

The Feynman path integrals for the magnetic Schroedinger equations are defined mathematically, in particular, with polynomially growing potentials in the spatial direction. For example, we can handle electromagnetic potentials $(V,A_{1},A_{2},...,A_{d})$ such that $V(t,x) = |x|^{2(l+1)} + $`` a polynomial of degree $(2l + 1)$ in $x$ " ($l = 0,1,2,...$) and $A_{j}(t,x)$ are polynomials of degree $l$ in $x$. The Feynman path integrals are defined as $L^2$-valued continuous functions with respect to the time variable.

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Wataru Ichinose. 2019-07-22. On the Feynman path integral for the magnetic Schroedinger equation with a polynomially growing electromagnetic potential. https://doi.org/10.1142/s0129055x20500038

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