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Journal of KPRU Science Mathematics and Technology

Evaluation of Time-Dependent Displacement of Particle Bound in Anharmonics Oscillator Potential Perturb by Electrostatic External Force via Heisenberg Picture Method

Artit Hutem

Published Dec 26, 2024• 0 citations
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Abstract

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 .

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รายละเอยดโครงการวจยเรอง การคำนวณหาการกระจดของอนภาคทถกกกในบอศกยแนบแอนฮารมอนกสทถกรบกวนดวยแรงภายนอกเปนฟงกชนของวลาโดยใชวธภาพไฮเซนเบรก (Evaluation of Time-Dependent Displacement of particle Bound in Anharmonics Oscillator potential perturb by external force via Heisen berg Picture Method)
รายละเอยดโครงการวจยเรอง การคำนวณหาการกระจดของอนภาคทถกกกในบอศกยแนบแอนฮารมอนกสทถกรบกวนดวยแรงภายนอกเปนฟงกชนของวลาโดยใชวธภาพไฮเซนเบรก (Evaluation of Time-Dependent Displacement of particle Bound in Anharmonics Oscillator potential perturb by external force via Heisen berg P...
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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.
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 .