The One-Dimensional Harmonic Oscillator

John P. Lowe

Xie Yu-peng

Linear harmonic oscillator takes an important role in quantum mechanics.Many systems can be taken approximately as of linear harmonic oscillator.Consequently,the study on linear harmonic oscillator is significant in many ways.Using methods of formula and perturbation,this paper finds out the energy eigenvalue of one-dimensional linear harmonic oscillator in weak electric field,and presents clearly two typical solutions for the energy level of one-dimensional linear harmonic oscillator in weak electric field.

John P. Lowe

B. G. Wybourne

Abstract The symmetry properties of bosons and fermions in a one‐dimensional harmonic oscillator are explored. It is shown that there is a one‐to‐one correspondence between the counts of the maximal spin states states formed by N‐noninteracting bosons and fermions in a one‐dimensional harmonic oscillator. © 2002 Wiley Periodicals, Inc. Int J Quantum Chem, 2002

Adam B. Cahaya

One dimensional quantum harmonic oscillator is well studied in elementary textbooks of quantum mechanics. The wave function of one-dimensional oscillator harmonic can be written in term of Hermite polynomial. Due to the symmetry of the spring energy, the wave functions of two-dimensional and three-dimensional harmonic oscillators can be written as products of the one-dimensional case. Because of that, the wave functions of two- and three-dimensional cases are focused on cartesian coordinates. In this article, we utilize polar and spherical coordinates to describe the wave function of two- and three-dimensional harmonic oscillators, respectively. The radial part of the wave functions can be written in term of associated Laguerre polynomials.

John P. Lowe