Bender-Dunne Orthogonal Polynomials, Quasi-Exact Solvability and Asymptotic Iteration Method for Rabi Hamiltonian

We present a method for obtaining the quasi-exact solutions of the Rabi Hamiltonian in the framework of the asymptotic iteration method. The energy eigenvalues, the eigenfunctions and the associated Bender-Dunne orthogonal polynomials are deduced. The latter prove to have a nonpositive definite norm.Comment: 10 page

The effective potential and resummation procedure to multidimensional complex cubic potentials for weak and strong-coupling

The method for the recursive calculation of the effective potential is applied successfully in case of weak coupling limit (g tend to zero) to a multidimensional complex cubic potential. In strong-coupling limit (g tend to infinity), the result is resumed using the variational perturbation theory (VPT). It is found that the convergence of VPT-results approaches those expected.Comment: 19 pages, 0 figur