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Title Accuracy of the Wentzel-Kramers-Brillouin (WKB) Quantization Condition for Symmetric Power Law Potentials Author Revision date 2013-09-30 Description It is well known that the WKB quantization condition gives the correct energy levels for the quantum mechanical simple harmonic oscillator (quadratic potential) and that it gives a good approximation in general for states with a large quantum number. For symmetric power law potentials V(x) [Proportional] | x ^p | , it is shown that the WKB energy levels [Proportional] (n + 1/2)^((2p)/(2+p)) where n is the quantum number. Furthermore, the value of the WKB prediction divided by the actual value for the ground state energy decreases with increasing p, with values of approximately 1.09, 1.0, 0.90 ,0.82, 0.75,and 0.25 for p = 1, 2, 3, 4, 5, [Infinity]. The accuracy of the inverse WKB quantization condition for some of these potentials is also discussed. Subjects Applied Mathematics > Numerical Methods > Approximation Theory Mathematics > Calculus and Analysis > Differential Equations Science > Physics > Quantum Physics Wolfram Technology > Kernel > Numerics Wolfram Technology > Programming > Symbolic Computation Keywords Quantum Mechanics, WKB Approximation, Quantized Energy Levels Downloads WKB_accuracy.nb (176.5 KB) - Mathematica Notebook

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