Abstract
The semiclassical surface-of-section method is extended to treat a three-dimensional model problem. Integration of classical trajectories generates four-dimensional phase-space surfaces; two-dimensional interpolation on each hypersurface provides an exact Poincaré surface of section. Numerical quadrature provides classical actions and semiclassical quantum numbers. The energy, a function of three non-integer quantum numbers, is interpolated to integer values of the quantum numbers to obtain the semiclassical eigenvalue spectrum. Results for a model problem are compared with quantum variational calculations. Twenty-two eigenvalues were obtained with 17 trajectories.
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