Accuracy of the WKB approximation: the case of general quartic potential

Details Accuracy of the WKB approximation: the case of general quartic potential Accuracy of the WKB approximation: the case of general quartic potential

2000-03-24

arxiv.org/abs/nlin/0003051v1

Nonlinear Sciences

Chaotic Dynamics

20 pages, 8 figures, 2 tables, PTP LaTeX style, to be published in the proceedings of the conference/summer school 'Let's Face

Scientific paper

10.1143/PTPS.139.214

We analyse the accuracy of the approximate WKB quantization for the case of general one-dimensional quartic potential. In particular, we are interested in the validity of semiclassically predicted energy eigenvalues when approaching the limit $E\to \infty$, and in the accuracy of low lying energy levels below the potential barrier in the case of generally asymmetric double-well quartic potential. In the latter case, using the standard WKB quantization an unnatural localization of eigenstates due to the negligence of tunneling is implied and thus the validity of semiclassics is uncertain. In all computations the higher order corrections to the leading semiclassical approximation are included using the complex contour integration technique. We show that these corrections can improve accuracy of semiclassical approximation greatly by many orders of magnitude.

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