The Relation Between One—to—One Correspondent Orthonormal Eigenstates of H^0 and H（λ）=H^0＋λV

The relation between one-to-one correspondent orthonormal eigenstates of H0 and 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 |φi(λ)> and|φ0m(i)>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.