Exactness of SWKB for Shape Invariant Potentials
arXiv:2005.06683 · doi:10.1016/j.physleta.2020.126722
Abstract
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.
arXiv comment15 pages, 2 figures; Accepted for publication in Physics Letters A
References in corpus (14)
- Exceptional orthogonal polynomials, exactly solvable potentials and supersymmetry
- Exactly Solvable Quantum Mechanics and Infinite Families of Multi-indexed Orthogonal Polynomials
- Another set of infinitely many exceptional (X_{\ell}) Laguerre polynomials
- Solvable Rational Potentials and Exceptional Orthogonal Polynomials in Supersymmetric Quantum Mechanics
- Infinitely many shape invariant discrete quantum mechanical systems and new exceptional orthogonal polynomials related to the Wilson and Askey-Wilson polynomials
- Riccati equation, Factorization Method and Shape Invariance
- Generation of a Complete Set of Supersymmetric Shape Invariant Potentials from an Euler Equation
- Novel Enlarged Shape Invariance Property and Exactly Solvable Rational Extensions of the Rosen-Morse II and Eckart Potentials
- Revisiting (quasi-)exactly solvable rational extensions of the Morse potential
- Extensions of solvable potentials with finitely many discrete eigenstates
- Shape Invariant potentials depending on n parameters transformed by translation
- N-fold Supersymmetry and Quasi-solvability Associated with X_2-Laguerre Polynomials
- Quasi-classical path integral approach to supersymmetric quantum mechanics
- The Supersymmetric WKB Formalism is Not Exact for All Additive Shape Invariant Potentials
Cited by in corpus (8)
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- SWKB Quantization Condition for Conditionally Exactly Solvable Systems and the Residual Corrections
- Generalized Langer Correction and the Exactness of WKB for all Conventional Potentials
- Infinite families of shape invariant potentials with n parameters subject to translation
- Quantum Hamilton-Jacobi Quantization and Shape Invariance