Unitary expansion of the time evolution operator

TL;DR

This paper introduces a method to approximate the time evolution operator in quantum mechanics by expressing it as a finite product of explicit unitary operators, allowing controlled truncation for practical computations.

Contribution

It presents a novel expansion technique for the unitary evolution operator, enabling systematic approximations with explicit unitary components.

Findings

Effective truncation of the expansion for practical use

Explicit construction of unitary operators for specific cases

Demonstrated applicability through examples

Abstract

We propose an expansion of the unitary evolution operator, associated to a given Schr\"odinger equation, in terms of a finite product of explicit unitary operators. In this manner, this unitary expansion can be truncated at the desired level of approximation, as shown in the given examples.