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The addition of the supersymmetric method provides several appealing qualities to this method. First, it is known that, by construction, the ground state energy will be exactly estimated. This is an improvement over the standard WKB approximation, which often has weaknesses at lower energies. Another
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property is that a class of potentials known as shape invariant potentials have their energy spectra estimated exactly by this first-order condition.
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The SWKB approximation then writes the Born–Sommerfeld quantization condition from the WKB approximation in terms of
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Cooper, Fred; Khare, Avinash; Sukhatme, Uday (1995). "Supersymmetry and
Quantum Mechanics".
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445:{\displaystyle {\frac {1}{\hbar }}\int _{b}^{a}dx\,{\sqrt {2m(E_{n}-W^{2}(x))}}=n\pi }
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The SWKB approximation for unbroken supersymmetry, to first order in
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systems. Using the supersymmetric method, there are potentials
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that can be expressed in terms of a superpotential,
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609:{\displaystyle W^{2}(a)=W^{2}(b)=E_{n}}
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