scholarly journals Quasi exactly solvable extension of Calogero model associated with exceptional orthogonal polynomials

2017 ◽  
Vol 380 ◽  
pp. 206-212 ◽  
Author(s):  
B. Basu-Mallick ◽  
Bhabani Prasad Mandal ◽  
Pinaki Roy
Keyword(s):  
Orthogonal Polynomials ◽  
Calogero Model ◽  
Exactly Solvable ◽  
Solvable Extension ◽  
Exceptional Orthogonal Polynomials

scholarly journals HIGHER-ORDER SUSY, EXACTLY SOLVABLE POTENTIALS, AND EXCEPTIONAL ORTHOGONAL POLYNOMIALS

2011 ◽  
Vol 26 (25) ◽  
pp. 1843-1852 ◽  
Author(s):  
C. QUESNE
Keyword(s):  
Quantum Mechanics ◽  
Orthogonal Polynomials ◽  
Higher Order ◽  
Wave Functions ◽  
Supersymmetric Quantum Mechanics ◽  
Solvable Potentials ◽  
Exactly Solvable Potentials ◽  
Exactly Solvable ◽  
Exceptional Orthogonal Polynomials

Exactly solvable rationally-extended radial oscillator potentials, whose wave functions can be expressed in terms of Laguerre-type exceptional orthogonal polynomials, are constructed in the framework of kth-order supersymmetric quantum mechanics, with special emphasis on k = 2. It is shown that for μ = 1, 2, and 3, there exist exactly μ distinct potentials of μth type and associated families of exceptional orthogonal polynomials, where μ denotes the degree of the polynomial gμ arising in the denominator of the potentials.

scholarly journals RATIONALLY-EXTENDED RADIAL OSCILLATORS AND LAGUERRE EXCEPTIONAL ORTHOGONAL POLYNOMIALS IN kTH-ORDER SUSYQM

2011 ◽  
Vol 26 (32) ◽  
pp. 5337-5347 ◽  
Author(s):  
C. QUESNE
Keyword(s):  
Quantum Mechanics ◽  
Orthogonal Polynomials ◽  
Laguerre Polynomials ◽  
Supersymmetric Quantum Mechanics ◽  
Shape Invariance ◽  
Order Analysis ◽  
First Order ◽  
Exactly Solvable ◽  
Exceptional Orthogonal Polynomials ◽  
Differential Relations

A previous study of exactly solvable rationally-extended radial oscillator potentials and corresponding Laguerre exceptional orthogonal polynomials carried out in second-order supersymmetric quantum mechanics is extended to kth-order one. The polynomial appearing in the potential denominator and its degree are determined. The first-order differential relations allowing one to obtain the associated exceptional orthogonal polynomials from those arising in a (k-1)th-order analysis are established. Some nontrivial identities connecting products of Laguerre polynomials are derived from shape invariance.

scholarly journals GENERALIZED RAYLEIGH AND JACOBI PROCESSES AND EXCEPTIONAL ORTHOGONAL POLYNOMIALS

2013 ◽  
Vol 27 (24) ◽  
pp. 1350135 ◽  
Author(s):  
C.-I. CHOU ◽  
C.-L. HO
Keyword(s):  
Orthogonal Polynomials ◽  
Exactly Solvable ◽  
Exceptional Orthogonal Polynomials ◽  
Jacobi Process ◽  
Fokker Planck Equations ◽  
Rayleigh Process ◽  
Fokker Planck

We present four types of infinitely many exactly solvable Fokker–Planck equations, which are related to the newly discovered exceptional orthogonal polynomials. They represent the deformed versions of the Rayleigh process and the Jacobi process.

scholarly journals Quasi‐exactly solvable systems and orthogonal polynomials

1996 ◽  
Vol 37 (1) ◽  
pp. 6-11 ◽  
Author(s):  
Carl M. Bender ◽  
Gerald V. Dunne
Keyword(s):  
Orthogonal Polynomials ◽  
Exactly Solvable
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