Supersymmetry-inspired WKB approximation in quantum mechanics

Dutt, Ranabir ; Khare, Avinash ; Sukhatme, Uday P. (1991) Supersymmetry-inspired WKB approximation in quantum mechanics American Journal of Physics, 59 (9). pp. 723-727. ISSN 0002-9505

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The supersymmetry-inspired WKB approximation (SWKB) in quantum mechanics is discussed in detail. The SWKB method can be easily applied to any potential whose ground-state wave function is known. It yields eigenvalues that are exact for large quantum numbers n (as any WKB approximation should in the classical limit). Furthermore, for the important special case of "shape-invariant" potentials, the SWKB approach gives the exact analytic expressions for the entire bound-state spectra. A study of some nonshape-invariant, but solvable, potentials suggests that shape invariance is not only sufficient but perhaps even necessary for the SWKB approximation to be exact. A comparison of the WKB and SWKB predictions for the bound-state spectra of a number of potentials reveals that in many cases the SWKB approach does better than the usual WKB approximation.

Item Type:Article
Source:Copyright of this article belongs to American Institute of Physics.
Keywords:Supersymmetry; Quantum Mechanics; WKB Approximation; Bound State; Ground States; Schroedinger Equation
ID Code:82044
Deposited On:09 Feb 2012 05:09
Last Modified:18 May 2016 23:23

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