A new derivation of Judds isolated exact solutions for E ⊗ e and Γ8 ⊗ τ2 Jahn-Teller systems

The Longuet-Higgins recurrence relations for the dynamical J-T problem are equivalent to a system of two ordinary linear first order differential equations. After Laplace transformation, recurrence relations for power series are found, which, in contradistinction to the original ones, are very simple. On the baselines they allow for terminating series, which give Judds isolated exact solutions plus the solution which asymptotically approaches the baseline for infinite coupling strength.