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Schrödinger equation; exactly solvable potentials; supersymmetry; orthogonal polynomials; exceptional orthogonal polynomials.

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.

K V S Shiv Chaitanya¹ S Sree Ranjani² Prasanta K Panigrahi³ R Radhakrishnan⁴ V Srinivasan⁴

1. BITS Pilani, Hyderabad Campus, Jawahar Nagar, Shameerpet Mandal, Hyderabad 500 078, India
2. Faculty of Science and Technology, ICFAI Foundation for Higher Education, Donthanapally, Hyderabad 501 203, India
3. Indian Institute of Science Education and Research (IISER), Kolkata, Mohanpur Campus, Nadia 714 252, India
4. Department of Theoretical Physics, University of Madras, Guindy Campus, Chennai 600 025, India

Published

July 2015

Manuscript received

17 April 2014

Accepted

28 May 2014

Early published

14 January 2015