TY - JOUR
T1 - A simple harmonic quantum oscillator
T2 - fractionalization and solution
AU - Batiha, Iqbal M.
AU - Jebril, Iqbal H.
AU - Al-Nana, Abeer A.
AU - Alshorm, Shameseddin
N1 - Publisher Copyright:
© 2024 Iqbal M. Batiha, et al.
PY - 2024
Y1 - 2024
N2 - 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.
AB - 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.
KW - Adomian decomposition
KW - harmonic oscillator
KW - Hermite polynomial
UR - http://www.scopus.com/inward/record.url?scp=85190307542&partnerID=8YFLogxK
U2 - 10.21595/mme.2024.23904
DO - 10.21595/mme.2024.23904
M3 - Article
AN - SCOPUS:85190307542
SN - 2351-5279
VL - 10
SP - 26
EP - 34
JO - Mathematical Models in Engineering
JF - Mathematical Models in Engineering
IS - 1
ER -