scholarly journals Exceptional orthogonal polynomials, exactly solvable potentials and supersymmetry

2008 ◽  
Vol 41 (39) ◽  
pp. 392001 ◽  
Author(s):  
C Quesne
Keyword(s):  
Orthogonal Polynomials ◽  
Solvable Potentials ◽  
Exactly Solvable Potentials ◽  
Exactly Solvable ◽  
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 SHAPE INVARIANT POTENTIALS IN ARBITRARY D DIMENSIONS ASSOCIATED WITH EXCEPTIONAL Xm POLYNOMIALS

2017 ◽  
Vol 57 (6) ◽  
pp. 477 ◽  
Author(s):  
Rajesh Kumar Yadav ◽  
Nisha Kumari ◽  
Avinash Khare ◽  
Bhabani Prasad Mandal
Keyword(s):  
Canonical Transformation ◽  
Bound State ◽  
Invariance Property ◽  
Shape Invariance ◽  
Point Canonical Transformation ◽  
Solvable Potentials ◽  
Shape Invariant ◽  
Exactly Solvable Potentials ◽  
Exactly Solvable ◽  
Exceptional Orthogonal Polynomials

Rationally extended shape invariant potentials in arbitrary D-dimensions are obtained by using point canonical transformation (PCT) method. The bound-state solutions of these exactly solvable potentials can be written in terms of <em>X<sub>m</sub></em> Laguerre or <em>X<sub>m</sub></em> Jacobi exceptional orthogonal polynomials. These potentials are isospectral to their usual counterparts and possess translationally shape invariance property.

scholarly journals Quasi‐exactly solvable potentials on the line and orthogonal polynomials

1996 ◽  
Vol 37 (8) ◽  
pp. 3954-3972 ◽  
Author(s):  
Federico Finkel ◽  
Artemio González‐López ◽  
Miguel A. Rodríguez
Keyword(s):  
Orthogonal Polynomials ◽  
Solvable Potentials ◽  
Exactly Solvable Potentials ◽  
Exactly Solvable

The quasi-exactly solvable potentials method applied to the three-body problem

2007 ◽  
Vol 322 (5) ◽  
pp. 1034-1042 ◽  
Author(s):  
F. Chafa ◽  
A. Chouchaoui ◽  
M. Hachemane ◽  
F.Z. Ighezou
Keyword(s):  
Body Problem ◽  
Three Body Problem ◽  
Solvable Potentials ◽  
Exactly Solvable Potentials ◽  
Exactly Solvable ◽  
Three Body

scholarly journals SPECTRUM OF THE RELATIVISTIC PARTICLES IN VARIOUS POTENTIALS

2005 ◽  
Vol 20 (12) ◽  
pp. 911-921 ◽  
Author(s):  
RAMAZAN KOÇ ◽  
MEHMET KOCA
Keyword(s):  
Quantum Mechanics ◽  
Hypergeometric Functions ◽  
Two Dimensions ◽  
Dirac Oscillator ◽  
Confluent Hypergeometric Functions ◽  
Solvable Potentials ◽  
Exactly Solvable Potentials ◽  
Exactly Solvable ◽  
Nonrelativistic Quantum Mechanics ◽  
Relativistic Particles

We extend the notion of Dirac oscillator in two dimensions, to construct a set of potentials. These potentials become exactly and quasi-exactly solvable potentials of nonrelativistic quantum mechanics when they are transformed into a Schrödinger-like equation. For the exactly solvable potentials, eigenvalues are calculated and eigenfunctions are given by confluent hypergeometric functions. It is shown that, our formulation also leads to the study of those potentials in the framework of the supersymmetric quantum mechanics.

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