An alternative approach to exact wave functions for time-dependent coupled oscillator model of charged particle in variable magnetic field

TL;DR

This paper introduces an alternative method using canonical and unitary transformations to derive exact wave functions for a time-dependent coupled oscillator system of a charged particle in a variable magnetic field, providing a new approach to solving such quantum systems.

Contribution

It presents a novel approach employing alternative canonical and unitary transformations to obtain exact solutions for the time-dependent coupled oscillator model in a magnetic field.

Findings

Derived exact wave functions for the system.

Validated the method with a specific example.

Recovered known results as a special case.

Abstract

A general treatment of the quantal time-dependent coupled oscillators in presence of the variable magnetic field is presented. The treatment is based on the use of an alternative canonical transformations, time-dependent unitary transformations and the invariant methods. Exact wave functions for Schr\"{o}dinger equations of this system are constructed.We applied our theory to a particular case and, co,sequently, showed that our results recovers to the perviously known one.