@article{JI2025, 
author = {Huaiyu JI and Zijun ZHANG and Hua ZHENG and Hui SUN},
title = {STUDY ON THE EQUIVALENCE BETWEEN COORDINATE REPRESENTATION AND MOMENTUM REPRESENTATION FOR ONE-DIMENSIONAL HARMONIC OSCILLATOR},
year = {2025},
journal = {Physics and Engineering},
volume = {35},
number = {3},
pages = {14-19},
keywords = {one-dimensional harmonic oscillator, Hermitian polynomial, generating function, Fourier transform},
url = {https://www.sciopen.com/article/10.26599/PHYS.2025.9320304},
doi = {10.26599/PHYS.2025.9320304},
abstract = {The one-dimensional harmonic oscillator is one of the few models in quantum mechanics that can be solved analytically, and it is used to exam the theories and methods of quantum mechanics, possessing rich connotations. Using the Fourier transform and the generating function of Hermite polynomials, the transformation from the eigenfunction in the coordinate representation to that in the momentum representation for a one-dimensional harmonic oscillator has been achieved. The equivalence and connection between the two representations for describing a one-dimensional harmonic oscillator are verified. The eigenenergies and eigenfunctions of the one-dimensional harmonic oscillator in the coordinate representation and momentum representation are also obtained by using the algebraic solution method, respectively. The equivalence of the two representations is further discussed. The idea of psolving physical problems in higher dimensional spaceq is emphasized, which deepens students' understanding of quantum mechanics and stimulates their interest in learning.}
}