Klenner, N. Treatment of the generalized E\(\times \epsilon\) Jahn-Teller Hamiltonian in polar coordinates. (English) Zbl 0614.70018 J. Phys. A 19, 3823-3830 (1986). 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 Cited in 1 Document 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 Keywords:Neumann series; Jahn-Teller effect; vibrational mode; electronic level; Jahn-Teller Hamiltonian; configuration space; radial oscillators; recurrence relations; linear first-order ordinary differential equations; Laplace transformation; exact solutions PDFBibTeX XMLCite \textit{N. Klenner}, J. Phys. A, Math. Gen. 19, 3823--3830 (1986; Zbl 0614.70018) Full Text: DOI