TY  - JOUR
T1  - Investigating Single Quantum Anharmonic Oscillator with Perturbation Theory
AU  - Nutku, Ferhat
AU  - Adalı, Büşra
PY  - 2023
DA  - December
DO  - 10.26650/PAR.2023.00011
JF  - Physics and Astronomy Reports
PB  - İstanbul Üniversitesi
WT  - DergiPark
SN  - 2980-3012
SP  - 93
EP  - 99
VL  - 1
IS  - 2
LA  - en
AB  - In this article, for pedagogical purposes we have discussed the application of nondegenerate perturbation theory up to the third order to compute energy eigenvalues and wave functions for the quantum anharmonic oscillator. Energy levels of a single quartic oscillator for 𝜆 values in range of 0.1-1 are given. Perturbed and non-perturbed wave functions of the levels up to the fourth excited level are compared. Ground, first and second excited energy levels are also calculated by applying finite differences method and, results are compared with the ones obtained via perturbation theory. It is found that perturbation theory gives comparable results only for a small 𝜆 parameter and for the ground state. The quartic term in the Hamiltonian of the anharmonic oscillator leads to a more effective confinement of the particle which is deduced from the plots of wavefunctions and probability distributions. Meanwhile, the number of zero crossing nodes of the wavefunctions increases as the energy level increases, which is an expected result for both the harmonic and anharmonic oscillator.
KW  - anharmonic oscillators
KW  - perturbation theory
KW  - quantum oscillator
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UR  - https://doi.org/10.26650/PAR.2023.00011
L1  - https://dergipark.org.tr/tr/download/article-file/3709935
ER  -