Quantum Mechanics with Explicit Time Dependence

TL;DR

This paper explores quantum Hamiltonians with explicit time dependence, identifying a class of models including a new exactly solvable harmonic oscillator with frequency inversely proportional to time.

Contribution

It introduces a new class of time-dependent quantum models and presents an exactly solvable harmonic oscillator with inverse time-dependent frequency.

Findings

Existence of a class of time-dependent quantum models with an analogue of the \\S equation

Introduction of a new exactly solvable harmonic oscillator model

Demonstration of solutions for models with explicit time dependence

Abstract

We investigate quantum mechanical Hamiltonians with explicit time dependence. We find a class of models in which an analogue of the time independent \S equation exists. Among the models in this class is a new exactly soluble model, the harmonic oscillator with frequency inversely proportional to time.