Double Anharmonic Potential Ax sup 2 +Bx sup 4 +Cx sup 6 and the Extended Continued Fractions

摘要

The sextic anharmonic-oscillator bound-state problem is considered, with an intention to extend its nonperturbative continued-fractional b > 0 solution to all couplings. Starting from its specific Hill-determinant treatment the authors employ a recurrent factorization of the related non-hermitean Hamiltonian and arrive at a complete nonperturbative solution represented in terms of the so-called extended continued fractions. The underlying less standard mathematical questions (singularities, convergence) are also clarified and, in particular, a systematic algebraic acceleration of convergence is proposed. In this way, both completion and improvement of the original constructions is achieved. 11 refs. (Atomindex citation 19:042337)