SEMICLASSICAL ENERGY QUANTIZATION OF ANHARMONIC POTENTIAL MOTION - COMPLEX TRAJECTORY CONTRIBUTIONS VERSUS HIGHER-ORDER CORRECTIONS

In the present investigation we assess the relevance of both classical ly forbidden phenomena and higher-order asymptotic contributions for t he semiclassical energy quantization of a particle in the anharmonic o scillator potential V(x) = x2/2 + lambdax4. We propose an iterative me thod (Iq) for obtaining higher-order semiclassical corrections, which is similar to the WKB and phase-integral methods in the lowest order, but in higher orders the approximation differs significantly. A 'primi tive' Bohr-Sommerfeld energy quantization is compared with a mote comp lete semiclassical quantization, taking into account both complex traj ectory contributions and higher-order (quantal) corrections.