Non-Adiabatic Solution to the Time Dependent Quantum Harmonic Oscillator

TL;DR

This paper introduces a non-adiabatic method for solving the time-dependent quantum harmonic oscillator using Schwinger Variational Principle, allowing for more general frequency variations with minimal smoothness assumptions.

Contribution

The authors develop a novel non-adiabatic solution approach that relaxes the usual smoothness constraints on the frequency function, broadening the applicability of quantum oscillator solutions.

Findings

Provides a new solution framework for non-adiabatic quantum oscillators

Allows frequency functions with only continuous first derivatives or finite discontinuities

Expands the theoretical understanding of time-dependent quantum systems

Abstract

Using Schwinger Variational Principle we solve the problem of quantum harmonic oscillator with time dependent frequency. Here, we do not take the usual approach which implicitly assumes an adiabatic behavior for the frequency. Instead, we propose a new solution where the frequency only needs continuity in its first derivative or to have a finite set of removable discontinuities.