Dynamics of Particle in a Box in Time Varying Potential Due to Chirped Laser Pulse

Brijender Dahiya,Vinod Prasad

doi:10.4236/jmp.2010.16053

Abstract

We describe a computational method for simulating the time dependent quantum mechanical system inter-acting with external field. In this method the Schrodinger equation is solved by expanding the wave function in the basis set of unperturbed Hamiltonian. The expansion yields a set of coupled first order differential equation. For expansion coefficients, the coupled channel method is applied to a particle in a box interacting with external field in the form of chirped laser pulse. The pulse shape is taken as Gaussian. We study the ef-fect of different pulse parameters i.e. chirp rate, intensity, center frequency, box length and laser duration on the dynamics of the particle. Many interesting results are obtained and explained.

Highlights

Quantum mechanics [1,2] is the fundamental base for several branches in Physics and particle in a box is one of the fundamental problems of quantum mechanics
We describe a computational method for simulating the time dependent quantum mechanical system interacting with external field
We study the effect of different pulse parameters i.e. chirp rate, intensity, center frequency, box length and laser duration on the dynamics of the particle

Summary

Introduction

Quantum mechanics [1,2] is the fundamental base for several branches in Physics and particle in a box is one of the fundamental problems of quantum mechanics. We have studied dynamics of a particle in a box in time varying external field/potential. This time varying field is achieved using a chirped laser pulse. Wang and Champagne [3] have studied the interaction of Gaussian laser pulse with the particle in a box. The selection depends on the system with which the laser pulse is interacting and other parameters of pulse e.g. intensity, center frequency, pulse width etc No work for such type of problem has been published earlier. Transition probabilities for different states as a function of time, chirp rate, box length and laser center frequency.

The Coupled Channel Method

Particle in a Box in Chirped Laser Field

Computational Analysis

Results

Conclusions