A Fundamental Solution to the Schr\"odinger Equation with Doss Potentials and its Smoothness

@article{Grothaus2015AFS,
  title={A Fundamental Solution to the Schr\"odinger Equation with Doss Potentials and its Smoothness},
  author={Martin Grothaus and Felix Riemann},
  journal={arXiv: Mathematical Physics},
  year={2015}
}
We construct a fundamental solution to the Schr\"odinger equation for a class of potentials of polynomial type by a complex scaling approach as in [Doss1980]. The solution is given as the generalized expectation of a white noise distribution. Moreover, we obtain an explicit formula as the expectation of a function of Brownian motion. This allows to show its differentiability in the classical sense. The admissible potentials may grow super-quadratically, thus by a result from [Yajima1996] the… 
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