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

Abstract

The quantum states of time-dependent coupled oscillator model for charged particles subjected to variable magnetic field are investigated using the invariant operator methods. To do this, we have taken advantage of an alternative method, so-called unitary transformation approach, available in the framework of quantum mechanics, as well as a generalized canonical transformation method in the classical regime. The transformed quantum Hamiltonian is obtained using suitable unitary operators and is represented in terms of two independent harmonic oscillators which have the same frequencies as that of the classically transformed one. Starting from the wave functions in the transformed system, we have derived the full wave functions in the original system with the help of the unitary operators. One can easily take a complete description of how the charged particle behaves under the given Hamiltonian by taking advantage of these analytical wave functions.

Dynamical normal modes for time-dependent Hamiltonians in two dimensions

“…Moreover they are easy to understand, visualize, and implement. More general (mixed) canonical transformations have not been considered in this paper, but they are in principle possible [24][25][26][27][28][29] and will be discussed elsewhere. Generically their physical meaning, definition, and practical use become more involved, so only simplified potential configurations and dynamics are typically worked out explicitly [24][25][26][27][28][29].…”

Soluções clássicas de sistemas acoplados dependentes do tempo

“…Recentemente, Menouar et al [3,4] calcularam a função de onda de dois sistemas que descrevem o movimento de uma partícula em um campo magnético variável. Na Ref.…”

“…[3] os autores consideraram o termo de acoplamento estático, xy, enquanto na Ref. [4] eles consideraram o termo de acoplamento dinâmico, p x p y . As soluções encontradas pelos autores foram expressas em termos de uma variável que satisfaz a equação de Milne-Pinney [5,6].…”

Quantization of time-dependent singular potential systems: Non-central potential in three dimensions

“…1 The wave functions that satisfy the Schrödinger equation for the time-dependent coupled oscillators have been computed using the methods of unitary transformation and canonical transformation. [2][3][4] Coherent states for a time-dependent Morse oscillator are investigated using the Feinberg-Horodecki quantal equation. 5 Exact solutions of the Schrödinger equation for quantum Dirac field in a time-dependent electric field have also been studied on the basis of the invariant theory.…”