摘要
Eigenvalue-solution to those Hamiltonians involving non-commutative coordinates is not easily obtained.In this paper we apply the invariant eigen-operator(IEO)method to solving the energy spectrum of the three-modeharmonic oscillator in non-commutative space with the coordinate operators satisfying cyclic commutative relations,[X_1,X_2]=[X_2,X_3]=[X_3,X_1]=iθ,and this method seems effective and concise.
Eigenvalue-solution to those Hamiltonians involving non-commutative coordinates is not easily obtained. In this paper we apply the invariant eigen-operator （IEO） method to solving the energy spectrmn of the three-mode harmonic oscillator in non-commutative space with the coordinate operators satisfying cyclic commutative relations, [X1, X2] = [X2, X3]=[X3, X1] = iθ, and this method seems effective and concise.
基金
the President Foundation of the Chinese Academy of Sciences
the Specialized Research Fund for the Doctoral Program of Higher Education
关键词
金属半导体超晶体
金费费米能级
电子能带
原子核
non-commutative coordinate space, invariant eigen-operator method, energy level
