Exact relation between the spectrum and the eigenfunctions of a generalized Jahn-Teller hamiltonian for different parameter values

A generalized E ? ? Jahn-Teller hamiltonian with a parameter δ (δ = ?1/4 in the JT case) is studied. As in the Jahn-Teller case, the angular momentum is a constant of the motion with the eigenvaluesj + 1/2 where j is a non-negative integer. For j fixed, consider two values δ₁ = ?j/2 ?1/2 and δ₂ = ?gd₁ ?1/2. The spectrum and the eigenfunctions for δ₂ are completely determined by the spectrum and the eigenfunctions for δ₁.