Exceptional orthogonal polynomials, QHJ formalism and SWKB quantization condition

Sree Ranjani, S. ; Panigrahi, P. K. ; Khare, A. ; Kapoor, A. K. ; Gangopadhyaya, A. (2012) Exceptional orthogonal polynomials, QHJ formalism and SWKB quantization condition Journal of Physics A: Mathematical and Theoretical, 45 (5). No pp. given. ISSN 1751-8113

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Official URL: http://iopscience.iop.org/1751-8121/45/5/055210

Related URL: http://dx.doi.org/10.1088/1751-8113/45/5/055210

Abstract

We study the quantum Hamilton-Jacobi (QHJ) equation of the recently obtained exactly solvable models, related to the newly discovered exceptional polynomials, and show that the QHJ formalism reproduces the exact eigenvalues and the eigenfunctions. The fact that the eigenfunctions have zeros and poles in complex locations leads to an unconventional singularity structure of the quantum momentum function p(x), the logarithmic derivative of the wavefunction, which forms the crux of the QHJ approach to quantization. A comparison of the singularity structure for these systems with the known exactly solvable and quasi-exactly solvable models reveals interesting differences. We find that the singularity structure of the momentum function for these new potentials lies between the above two distinct models, sharing similarities with both of them. This prompted us to examine the exactness of the supersymmetric Wentzel-Kramers-Brillouin (SWKB) quantization condition. The interesting singularity structure of p(x) and of the superpotential for these models has important consequences for the SWKB rule and in our proof of its exactness for these quantal systems.

Item Type:Article
Source:Copyright of this article belongs to Institute of Physics.
ID Code:83396
Deposited On:21 Feb 2012 07:15
Last Modified:19 May 2016 00:16

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