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A GENERALIZED QUANTUMANHARMONIC OSCILLATOR SHEN WENDA

S Wang

Published Jan 1, 1995• 0 citations
OpenAlex

Abstract

velocity-dependent quantum forced anharmonic cscillator is studied,and its exact solution is obtained by adopting the iteration mothod and the integral operators.Thestudyis carried on in operational form via the raising and lewering operators of the oseillator.The time developnment of the displacement and momentum operators of the quantumanharmonic osoillafor is presented in shape of a Laplace transform and.a subsequentinverse Laplace transform of suitable functionals.

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velocity-dependent quantum forced anharmonic cscillator is studied,and its exact solution is obtained by adopting the iteration mothod and the integral operators.Thestudyis carried on in operational form via the raising and lewering operators of the oseillator.The time developnment of the displacement and momentum operators of the quantumanharmonic osoillafor is presented in shape of a Laplace transform and.a subsequentinverse Laplace transform of suitable functionals.
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The present review is devoted to the study of certain aspects of anharmonic, time-dependent and damped oscillator(s) system using different theoretical techniques. A theoretical understanding of these systems is important for application in many problems in physics, mechanics and other fields. We discuss in detail the difficulties in the theoretical analysis of the problem. In particular we discuss here the regular, well-behaved perturbative solution, the large quantum number behaviour of anharmonic oscillator(s) using the technique of coherent states, exact solution of quantum anharmonic oscillators, the electromagnetic radiation emitted by a charged particle executing damped anharmonic oscillator motion using Krylov-Bogoliubov approximation method, use of invariants to obtain solution and coherent states of time-dependent oscillator(s), the derivation of perturbative frequencies of a damped coupled anharmonic oscillators system using suitable canonical transformation in the framework of Hamilton-Jacobi formalism and the quantisation and construction of coherent states of a damped oscillator using time-dependent operators.
In this research paper, we developed a theory and model of the forced simple harmonic oscillators in quantum mechanics system in a framework of a general approach to the Heisenberg picture. We can be used the time-dependent Hamiltonian for the forced simple harmonic oscillators. We use first-order ordinary linear differential equation to solve the time-dependent lowering operator and raising operator. We evaluate the lowering operator and raising operator as the function of time for particle mass depend on the parameter frequency of oscillation , the damping coefficient of particle bound in the simple harmonic oscillator potential, the initial force .