Cubature of multidimensional Schrödinger potential based on approximate approximations

We report here on some recent results obtained in collaboration with V. Maz'ya and G. Schmidt cite{LMS2017}. We derive semi-analytic cubature formulas for the solution of the Cauchy problem for the Schrödinger equation which are fast and accurate also if the space dimension is greater than or equal to 3. We follow ideas of the method of approximate approximations, which provides high-order semi-analytic cubature formulas for many important integral operators of mathematical physics. The proposed method is very efficient in high dimensions if the data allow separated representations.