The Relation Between One-to-One Correspondent Orthonormal Eigenstates of H0 and H(λ)=H0+λV**The project supported by National Basic Research Project “Nonlinear Science” of China

Abstract

The relation between one-to-one correspondent orthonormal eigenstates of H(λ)=H0+λV is carefully studied with general perturbation theory. Attention is particularly paid to the analyticity and its local destruction due to nonlinear resonance. Numerical results are given to show such possibility with a special Jacobi diagonalization method. The conclusions show that for the system H(λ) belonging to the same class as H0, the relation between one-to-one correspondent orthonormal eigenstates and can be expressed as an analytical unitary matrix which can be identified to the relevant quantum canonical transformation. But for the system H(λ) violated dynamical symmetry, the relation between one-to-one correspondent orthonormal eigenstates cannot be expressed as an analytical unitary matrix. Such a kind of unitary matrix cannot be taken as a quantum canonical transformation to define quantum mechanical quantities. This is a key point for studying the quantum chaos with the help of dynamical symmetry theory.