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PSRU Journal of Science and Technology

CREATION MODEL OF TIME-DEPENDENT LOWERING OPERATOR AND RAISING OPERATOR UNDER TIME-DEPENDENT EXTERNAL DAMPING FORCE SIMPLE HARMONIC OSCILLATOR : การสรางตวดำเนนการชนดสรางสถานะ และตวดำเนนการทำลายสถานะทเปนฟงกชนของเวลา

Piyarut Moonsri, Prisana Yakaw, Artit Hutem

Published Nov 30, 2020• 0 citations
OpenAlex

Abstract

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 .

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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 .
For this study, the researchers purposed to evaluate the Heisenberg equation of motion for the creation and annihilation operator under the force vibration simple harmonic oscillation. Instead of using the first-order ordinary differential equation to solve the Heisenberg equation of motion, the researchers got the time-dependent creation and annihilation operator under the time-dependent force vibration simple harmonic oscillation. The behavior of wave group in the creation and annihilation operator for image part is destroyed by increasing of the parameter value of .
We consider the time-dependent electrostatic force anharmonic oscillator potential in one-dimension. Here, we derive the existing Heisenberg equations of motion from Newton’s second law. We can be used the time-dependent Hamiltonian operator for the time-dependent electrostatic force anharmonic oscillator system. We use the principal of Wronskian method solve for solution of the expectation value of displacement operator for particle bound in anharmonic oscillator potential system. The behavior of the expectation value of displacement operator is wave oscillate depend on the parameter linear frequency, the initial charge, the initial electric, the parameter and .
The problem of a quantal harmonic oscillator with damping and a time-dependent frequency acted on by a time-dependent perturbative force is exactly solved. The wavefunctions are found in Schrödinger representation using the theory of explicitly time-dependent invariants and also by an expansion of the Feynman propagator. The propagator is obtained in exactly closed form by an explicit path integration of the classical Lagrangian. It is found that the wavefunctions and the propagator depend only on the solution of classical damped oscillator through a single function ρ (t). The function ρ (t) itself may be obtained as a solution of a second order nonlinear differential equation under the appropriate set of initial conditions.
The interaction picture of quantum mechanics is used to calculate the unitary time development operator for a harmonic oscillator subject to an arbitrary time-dependent force. The result is identical to that obtained from the more usual method of the Heisenberg equations of motion, except for a phase factor which the Heisenberg picture method is unable to determine. A simplified derivation of the phase factor is given in the adiabatic limit, as well as a discussion of some possible physical effects which would depend upon the phase factor.