Exactness of SWKB for shape invariant potentials

Exactness of SWKB for shape invariant potentials

•We prove that conventional potentials are SWKB-exact due to shape invariance.•We use the general superpotential form derived from additive shape invariance.•This general proof does not rely on the explicit form of superpotentials. The supersymmetry-based semiclassical method (SWKB) is known to prod...

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Veröffentlicht in:Physics letters. A 2020-10, Vol.384 (28), p.126722, Article 126722
Hauptverfasser: Gangopadhyaya, Asim, Mallow, Jeffry V., Rasinariu, Constantin, Bougie, Jonathan
Format: Artikel
Sprache:eng
Schlagworte:
Exactly solvable systems
Semiclassical approximation
Shape invariance
Supersymmetric quantum mechanics
SWKB
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Zusammenfassung:•We prove that conventional potentials are SWKB-exact due to shape invariance.•We use the general superpotential form derived from additive shape invariance.•This general proof does not rely on the explicit form of superpotentials. The supersymmetry-based semiclassical method (SWKB) is known to produce exact spectra for conventional shape invariant potentials. In this paper we prove that this exactness follows from their additive shape invariance.
ISSN:0375-9601
1873-2429
DOI:10.1016/j.physleta.2020.126722