Regularity of many-body Schr\"odinger evolution equation and its application to numerical analysis

Abstract

A decade ago, the mixed regularity of stationary many-body Schr\"o\-dinger equation has been studied by Harry Yserentant through the Pauli Principle and the Hardy inequality (Uncertainty Principle). In this article, we prove that the many-body evolution Schr\"odinger equation has a similar mixed regularity if the initial data $u_0$ satisfies the Pauli Principle. By generalization of the Strichartz estimates, our method also applies to the numerical approximation of this problem: based on these mixed derivatives, we design a new approximation which can hugely improve the computing capability especially in quantum chemistry.