Exceptional Polynomials and SUSY Quantum Mechanics
classification
🧮 math-ph
math.MPquant-ph
keywords
polynomialsexceptionalexistencenon-trivialodingerschrsolutionscorresponding
read the original abstract
We show that the existence of exceptional polynomials leads to the presence of non-trivial supersymmetry. The existence of these polynomials reveals several distinct isospectral potentials for the Schr\"odinger equation. All Schr\"odinger equations having Laguerre and Jacobi polynomials as their solutions, have non-trivial supersymmetric partners with corresponding exceptional polynomials as solutions.
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