On the Schrödinger equation with potentials which are Laplace transforms of measures (Q1275363)

The authors construct a pointwise solution for the time dependent Schrödinger equation on \(\mathbb{R}^d\) with potentials and initial conditions which can grow exponentially at infinity and belong to the class of smooth Laplace transforms of complex measures on \(\mathbb{R}^d\). The methods used are both analytic and probabilistic and the obtained result can be regarded as an extension of rigorously defined Feynman path integrals to the case of potentials which can strongly grow at infinity.