Exceptional polynomials and SUSY quantum mechanics

We show that for the quantum mechanical problem which admit classical Laguerre / Jacobi polynomials as solutions for the Schrödinger equations (SE), will also admit exceptional Laguerre /Jacobi polynomials as solutions having the same eigenvalues but with the ground state missing after a modificatio...

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Bibliographic Details
Published in:Pramāṇa 2015-07, Vol.85 (1), p.53-63
Main Authors: SHIV CHAITANYA, K V S, RANJANI, S SREE, PANIGRAHI, PRASANTA K, RADHAKRISHNAN, R, SRINIVASAN, V
Format: Article
Language:English
Subjects:
Astronomy
Astrophysics and Astroparticles
Observations and Techniques
Physics
Physics and Astronomy
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Summary:We show that for the quantum mechanical problem which admit classical Laguerre / Jacobi polynomials as solutions for the Schrödinger equations (SE), will also admit exceptional Laguerre /Jacobi polynomials as solutions having the same eigenvalues but with the ground state missing after a modification of the potential. Then, we claim that the existence of these exceptional polynomials leads to the presence of non-trivial supersymmetry.
ISSN:0304-4289
0973-7111
DOI:10.1007/s12043-014-0882-7