物理与工程2025，Vol.35Issue(3)：14-19,6.
一维谐振子坐标表象与动量表象的等价性
STUDY ON THE EQUIVALENCE BETWEEN COORDINATE REPRESENTATION AND MOMENTUM REPRESENTATION FOR ONE-DIMENSIONAL HARMONIC OSCILLATOR
摘要
Abstract
The one-dimensional harmonic oscillator is one of the few models in quantum me-chanics 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 gen-erating function of Hermite polynomials,the transformation from the eigenfunction in the co-ordinate representation to that in the momentum representation for a one-dimensional harmon-ic oscillator has been achieved.The equivalence and connection between the two representa-tions 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,respec-tively.The equivalence of the two representations is further discussed.The idea of"solving physical problems in higher dimensional space"is emphasized,which deepens students' under-standing of quantum mechanics and stimulates their interest in learning.关键词
一维谐振子/厄米多项式/生成函数/傅里叶变换Key words
one-dimensional harmonic oscillator/Hermitian polynomial/generating function/Fourier transform引用本文复制引用
纪怀昱,张子骏,郑华,孙辉..一维谐振子坐标表象与动量表象的等价性[J].物理与工程,2025,35(3):14-19,6.基金项目
国家自然科学基金(11905120). （11905120）
