Motion of Energy Levels and Energy Dependent Constants of Motion

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  • Motion of Energy Levels and Energy Depe

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Abstract

From the eigenvalue equation (H0+λV)|Ψn(λ)⟩=En(λ)|Ψn(λ)⟩ one can derive an autonomous system of first order differential equations for the eigenvalues En(λ) and the matrix elements Vmn(λ)=⟨Ψm(λ)|V|Ψn(λ)⟩ where λ is the independent variable. We investigate the case where the Hamiltonian H is given by a finite dimensional symmetric matrix and derive the energy dependent constants of motion. Furthermore we describe the connection with stationary state perturbation theory. Several open questions are also discussed.

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