WKB expansion for the angular momentum and the Kepler problem: from the torus quantization to the exact one

Abstract

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.Sq

16 pages plain Latex file, no figures. submitted to J. Phys. A

References in corpus (4)

• WKB to all orders and the accuracy of the semiclassical quantization
• Quasi-classical path integral approach to supersymmetric quantum mechanics
• Accuracy of the Semi--Classical Approximation: the Pullen Edmonds Hamiltonian
• Quantum corrections to the semiclassical quantization of a nonintegrable system

Cited by in corpus (10)

• Cosmological particle production and the precision of the WKB approximation
• Some properties of WKB series
• WKB to all orders and the accuracy of the semiclassical quantization
• On the Convergence of the WKB Series for the Angular Momentum Operator
• A mass formula for light mesons from a potential model
• Semiclassical analysis of Wigner functions
• Classical and Quantum Perturbation Theory for two Non--Resonant Oscillators with Quartic Interaction
• Three-component Fermi gas with SU(3) symmetry: BCS-BEC crossover in three and two dimensions
• Semiclassical Expansion for the Angular Momentum
• How Are Quantum Eigenfunctions of Hydrogen Atom Related To Its Classical Elliptic Orbits?