Open AccessA study on the first integrals of harmonic oscillators
Author(s) -
Ding Guang-Tao
Publication year - 2013
Publication title -
wuli xuebao
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.199
H-Index - 47
ISSN - 1000-3290
DOI - 10.7498/aps.62.064502
Subject(s) - slater integrals , harmonic oscillator , harmonic , irrational number , order of integration (calculus) , multiple integral , physics , mathematical analysis , anisotropy , mathematics , quantum mechanics , geometry
A concept of fundamental integrals of one-dimensional harmonic oscillator is presented, and other integrals can be constructed by use of fundamental integrals. The above concept and method are extended to multidimensional harmonic oscillators. By directly constructing other integrals from the fundamental integrals, it is proved that there are three independent time-independent integrals for all kinds of two-dimensional harmonic oscillators and there are 2n-1 independent time-independent integrals for n-dimensional harmonic oscillators. The characteristics of the anisotropic two-dimensional harmonic oscillator is discussed when the ratio between two frequencies is rational or irrational number.