  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.
