SIMULATING THE DYNAMICS OF A PARTICLE IN A QUANTUM MECHANICAL OSCILLATOR: A MULTIDIMENSIONAL WAVE FUNCTION APPROACH

Abstract

This research paper presents a simulation of a particle in a quantum mechanical oscillator, modeled as a multidimensional wave function. The simulation was created by solving the time-dependent Schrodinger equation, which was discretized in both the spatial and time domains, and then approximated using a finite difference method. The objective of this research was to gain a deeper understanding of the behavior of a particle in a quantum mechanical oscillator and to provide visualizations and calculations of relevant physical observables. Initial conditions for the wave function, such as a Gaussian wave packet, were chosen and parameters for the simulation, such as the spatial step size and total simulation time, were set. The results of the simulation showed the evolution of the wave function over time, providing a clear picture of the particles behavior within the potential well of the oscillator. Additionally, physical observables, such as the average position, average kinetic energy, and average potential energy, were calculated and used to validate the simulation and the predictions of quantum mechanics. In conclusion, this research provides a comprehensive understanding of the behavior of a particle in a quantum mechanical oscillator and highlights the importance of simulations in advancing our knowledge of quantum mechanics. The results of this research can contribute to various fields, such as quantum computation and quantum control, and have the potential to drive further breakthroughs in these fields. KEYWORDS: Quantum mechanical oscillator, particle behavior, multidimensional wave function, Schrödinger equation, finite difference method, physical observables, simulation, quantum mechanics, quantum computation, quantum control.