A new method for analyzing the time evolution of quantum mechanical systems

TL;DR

This paper introduces a novel approach to analyze quantum system dynamics by decomposing the Hamiltonian, demonstrated through an exactly solvable driven harmonic oscillator, revealing new nonspreading wave packets.

Contribution

It proposes a Hamiltonian decomposition method that clarifies quantum evolution and demonstrates its application to a driven harmonic oscillator, uncovering new wave packet phenomena.

Findings

Exact solution for driven harmonic oscillator.

Existence of nonspreading wave packets.

Method applicable to general Hamiltonian systems.

Abstract

We show a new method for analyzing the time evolution of the Schrodinger wave function phi(x,t). We propose the decomposition of the Hamiltonian as: H(t)=Hp(t)+Hc(t), where Hp(t)is the operator which does not change the state and therefore phi(x,t) is its eigenfunction, and Hc(t)is the operator that changes the state. With this decomposition, the time evolution of a wave function can be understood more clearly via the operator Hc(t). We illustrate this method by exactly solving the system of driven harmonic oscillator. We show that nonspreading wave packets exist in this system in addition to historically known paradigms. This method can be applied to analyze the time evolution of general Hamiltonian systems as well.