A geometric approach to time evolution operators of Lie quantum systems

TL;DR

This paper presents a geometric method for deriving time evolution operators in Lie quantum systems, providing a systematic approach and solving several quadratic Hamiltonian cases.

Contribution

It introduces a geometric framework to compute time evolution operators for Lie quantum systems, clarifying previous ad hoc methods and solving specific time-dependent quadratic Hamiltonians.

Findings

Developed geometric methods for time evolution operators

Explained previous ad hoc solution techniques

Solved multiple instances of time-dependent quadratic Hamiltonians

Abstract

Lie systems in Quantum Mechanics are studied from a geometric point of view. In particular, we develop methods to obtain time evolution operators of time-dependent Schrodinger equations of Lie type and we show how these methods explain certain ad hoc methods used in previous papers in order to obtain exact solutions. Finally, several instances of time-dependent quadratic Hamiltonian are solved.