Analyzing the Time Evolution of a Particle by Decomposes the Initial State Confinement in 1D Well into the Lowest Eigenstates Energy

Mubarak Hamad Oglah

doi:10.55544/jrasb.3.2.17

Authors

Mubarak Hamad Oglah Department of Mechanics Engineering, College of Al-Shirgat Engineering, Tikrit University, IRAQ. https://orcid.org/0000-0002-4368-5594

DOI:

https://doi.org/10.55544/jrasb.3.2.17

Keywords:

Schrodinger-equation, Particle-in-Box, Confinement, Time-evolution

Abstract

In this work, we obtained the time evolution of the wave function of a limited quantum system (1D Box), hence getting a mathematical model to describe the system. By using programming computes, it performs a time evolution that decomposes the initial state into the 2,10, and 20 lowest energy eigenstates. Finally, by comparing numerical de-composition coefficients for the wave function to the analytical values, it found the number of knots increases directly versus the energy of the particle's quantum state. As a result, the mean bending given by the second derivative which is proportional to the kinetic energy operator should increase. We found there is a negligible mean and standard deviation of the energy in units of the ground state energy.

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