On the von Neumann equation with time-dependent Hamiltonian. Part II: Applications

TL;DR

This paper applies a novel method to solve the Schrödinger equation with time-dependent Hamiltonians, providing new insights into the Bloch equations and harmonic oscillator, and demonstrating the approach's effectiveness in these classical quantum problems.

Contribution

It introduces a method to find all solutions from a single particular solution for time-dependent Hamiltonians, with new results in well-studied quantum systems.

Findings

New solutions for Bloch equations

Novel results for harmonic oscillator with time-dependent frequency

Method's effectiveness demonstrated in classical quantum models

Abstract

This second part deals with applications of a general method to describe the quantum time evolution determined by a Schroedinger equation with time-dependent Hamiltonian. A new aspect of our approach is that we find all solutions starting from one special solution. The two main applications are reviewed, namely the Bloch equations and the harmonic oscillator with time-dependent frequency. Even in these well-known examples some new results are obtained.