A simple harmonic quantum oscillator: fractionalization and solution

Iqbal M. Batiha, Iqbal H. Jebril, Abeer A. Al-Nana, Shameseddin Alshorm

Research output: Contribution to journalArticlepeer-review

4 Scopus citations

Abstract

A quantum mechanical system that mimics the behavior of a classical harmonic oscillator in the quantum domain is called a simple harmonic quantum oscillator. The time-independent Schrödinger equation describes the quantum harmonic oscillator, and its eigenstates are quantized energy values that correspond to various energy levels. In this work, we first fractionalize the time-independent Schrödinger equation, and then we solve the generated problem with the use of the Adomian decomposition approach. It has been shown that fractional quantum harmonic oscillators can be handled effectively using the proposed approach, and their behavior can then be better understood. The effectiveness of the method is validated by a number of numerical comparisons.

Original languageEnglish
Pages (from-to)26-34
Number of pages9
JournalMathematical Models in Engineering
Volume10
Issue number1
DOIs
StatePublished - 2024

Keywords

  • Adomian decomposition
  • harmonic oscillator
  • Hermite polynomial

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