210 research outputs found
High order WKB prediction of the energy splitting in the symmetric double well potential
The accuracy of the WKB approximation when predicting the energy splitting of
bound states in a double well potential is the main subject of this paper. The
splitting of almost degenerate energy levels below the top of the barrier
results from the tunneling and is thus supposed to be exponentially small. By
using the standard WKB quantization we deduce an analytical formula for the
energy splitting, which is the usual Landau formula with additional quantum
corrections. We also examine the accuracy of our and Landau formula numerically
for the case of the symmetric double well quartic potential.Comment: 8 pages, 2 figures, 1 table, PTP LaTeX style, to be published in the
proceedings of the conference/summer school 'Let's Face Chaos through
Nonlinear Dynamics', Maribor, Slovenia, June/July 1999, eds. M. Robnik et
al., Prog. Theor. Phys. Suppl. (Kyoto) 139 (2000
WKB expansion for the angular momentum and the Kepler problem: from the torus quantization to the exact one
We calculate the WKB series for the angular momentum and the
non--relativistic 3-dim Kepler problem. This is the first semiclassical
treatment of the angular momentum for terms beyond the leading WKB
approximation. We explain why the torus quantization (the leading WKB term) of
the full problem is exact, even if the individual torus quantization of the
angular momentum and of the radial Kepler problem separately is not exact.
PACS numbers: 03.65.-w, 03.65.Ge, 03.65.SqComment: 16 pages plain Latex file, no figures. submitted to J. Phys.
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