COHERENT STATE OF THE EXTENDED SCARF I POTENTIAL AND SOME OF ITS PROPERTIES

2013 ◽  
Vol 28 (28) ◽  
pp. 1350123
Author(s):  
N. AIZAWA ◽  
P. ROY
Keyword(s):  
Coherent State ◽  
Orthogonal Polynomials ◽  
Invariance Property ◽  
Shape Invariance ◽  
Exceptional Polynomials ◽  
Similarities And Differences ◽  
Exceptional Orthogonal Polynomials

Using shape invariance property we construct coherent state for a class of potentials containing Scarf I and its extensions, the solutions of the latter being given in terms of the recently discovered Jacobi-Xl type exceptional polynomials. It is shown that the coherent state possesses the property of resolution of unity and exhibits sub-Poissonian behavior. We then investigate the coherent state of Scarf I potential and its l = 1 extension in some detail to understand the similarities (and differences) between the exceptional orthogonal polynomials and their classical counterparts.

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 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 A Conjecture on Exceptional Orthogonal Polynomials

2012 ◽  
Vol 13 (4) ◽  
pp. 615-666 ◽  
Author(s):  
David Gómez-Ullate ◽  
Niky Kamran ◽  
Robert Milson
Keyword(s):  
Orthogonal Polynomials ◽  
Exceptional Orthogonal Polynomials

scholarly journals Algebraic calculations for spectrum of superintegrable system from exceptional orthogonal polynomials

2018 ◽  
Vol 391 ◽  
pp. 203-215 ◽  
Author(s):  
Md. Fazlul Hoque ◽  
Ian Marquette ◽  
Sarah Post ◽  
Yao-Zhong Zhang
Keyword(s):  
Orthogonal Polynomials ◽  
Superintegrable System ◽  
Exceptional Orthogonal Polynomials

scholarly journals Complex Exceptional Orthogonal Polynomials and Quasi-invariance

2016 ◽  
Vol 106 (5) ◽  
pp. 583-606 ◽  
Author(s):  
William A. Haese-Hill ◽  
Martin A. Hallnäs ◽  
Alexander P. Veselov
Keyword(s):  
Orthogonal Polynomials ◽  
Exceptional Orthogonal Polynomials
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