Accuracy of Semiclassical Methods for Shape Invariant Potentials

Abstract

We study the accuracy of several alternative semiclassical methods by computing analytically the energy levels for many large classes of exactly solvable shape invariant potentials. For these potentials, the ground state energies computed via the WKB method typically deviate from the exact results by about 10%, a recently suggested modification using nonintegral Maslov indices is substantially better, and the supersymmetric WKB quantization method gives exact answers for all energy levels.

7 pages, Latex, and two tables in postscript

References in corpus (4)

• Supersymmetry and Quantum Mechanics
• New Eaxactly Solvable Hamiltonians: Shape Invariance and Self-Similarity
• New Shape Invariant Potentials in Supersymmetric Quantum Mechanics
• Potentials with Two Shifted Sets of Equally Spaced Eigenvalues and Their Calogero Spectrum

Cited by in corpus (5)

• SWKB Quantization Condition for Conditionally Exactly Solvable Systems and the Residual Corrections
• A Parabolic Model for the Dimple Potentials
• Generalized Langer Correction and the Exactness of WKB for all Conventional Potentials
• A Semiclassical Approach to Level Crossing in Supersymmetric Quantum Mechanics
• Mass spectrum of Mesons via the WKB approximation method