@article{ZHANG2025, 
author = {Lei ZHANG and Feng XU and Yaqi HE},
title = {APPLICATIONS OF NUMERICAL CALCULATION IN TEACHING AND LEARNING ON HARMONIC OSCILLATOR},
year = {2025},
journal = {Physics and Engineering},
volume = {35},
number = {5},
pages = {75-83},
keywords = {harmonic oscillator, eigen problem, numerical simulation, finite difference method, finite element method},
url = {https://www.sciopen.com/article/10.26599/PHYS.2025.9320511},
doi = {10.26599/PHYS.2025.9320511},
abstract = {This paper uses one-dimensional and two-dimensional harmonic oscillators as examples for a learning mode that combines numerical computation with understanding quantum phenomena. It first applies the factorization method to derive analytical results for the one-dimensional harmonic oscillator’s eigen energy and eigenfunctions. Then, it discusses solving one-dimensional problems numerically with the finite difference method. Next, it extends these analytical and finite difference approaches to two-dimensional cases and proposes using one-dimensional Hamiltonian matrix calculations for efficient two-dimensional problem solving. Finally, it introduces the finite element method as an alternative for two-dimensional harmonic oscillators. To ensure accurate results with the finite difference and finite element methods, it stresses choosing a large enough simulation area to meet boundary conditions.}
}