Open AccessAn algebraic approach to the generalization of n-dimensional coupled harmonic oscillators system
Author(s) -
MJ Jin,
Liying Tan
Publication year - 2012
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.61.140301
Subject(s) - eigenfunction , hamiltonian (control theory) , eigenvalues and eigenvectors , generalization , harmonic oscillator , algebraic number , decoupling (probability) , commutation , quadratic equation , hamiltonian system , physics , mathematics , mathematical physics , mathematical analysis , quantum mechanics , voltage , mathematical optimization , geometry , control engineering , engineering
Using the quadratic form theory, we achieve the decoupling of systematic Hamiltonian of generalization of n-dimensional coupled harmonic oscillators and derive the diagonalized Hamiltonian by three linear transformations with keeping the commutation relations unchanged. The energy eigenvalue and the eigenfunction of the system are also obtained.