Quasi-Feynman formulas for a Schroedinger equation with a Hamiltonian equal to a finite sum of operators

Abstract

In this short communication I generalize the method of obtaining quasi-Feynman formulas described in my previous paper on that topic. The theorem presented allows to obtain the solution to the Cauchy problem for the Schr\"odinger equation with the Hamiltonian decomposed to a finite sum of operators. The concept of Chernoff tangency is used, and the solution is written in the form of a quasi-Feynman formula as before. Theorem proven is compared to known approximation theorems: Trotter's, Chernoff's, Butko-Schilling-Smolyanov's.