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

TL;DR

This paper extends the quasi-Feynman formula method to solve the Schrödinger equation with Hamiltonians expressed as finite sums of operators, using Chernoff tangency to derive solutions comparable to established approximation theorems.

Contribution

It generalizes the quasi-Feynman formula approach for Hamiltonians as finite sums, employing Chernoff tangency, and compares it to existing approximation theorems.

Findings

Derived a new quasi-Feynman formula for finite-sum Hamiltonians

Established the relation to Trotter's, Chernoff's, and other approximation theorems

Provided a theoretical framework for solving Schrödinger equations with complex Hamiltonians

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.