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Treatment of the generalized E\(\times \epsilon\) Jahn-Teller Hamiltonian in polar coordinates. (English) Zbl 0614.70018

In \(E\times \epsilon\) Jahn-Teller effect a vibrational mode \(\epsilon\) of a crystal interacts non-adiabatically with the electronic level E. The generalized \(E\times \epsilon\) Jahn-Teller Hamiltonian provides a mathematical model for describing the effect. The authors consider this Hamiltonian in a formulation which uses polar coordinates in configuration space. The vibronic part of the wave function is expanded in terms of a basis whose members are radial oscillators. They obtain simple recurrence relations which are equivalent to a system of linear first-order ordinary differential equations. A relationship with the system of differential equations obtained in the alternative treatment of [H. G. Reik, H. Nusser and L. A. Amarante Ribeiro [ibid. 15, 3491-3507 (1982)] is found and involves a Laplace transformation. The author obtains also the exact solutions in configuration space.
Reviewer: Ch.Sharma

MSC:

70H99 Hamiltonian and Lagrangian mechanics
82D20 Statistical mechanics of solids
70G10 Generalized coordinates; event, impulse-energy, configuration, state, or phase space for problems in mechanics
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