Cλ-Extended Oscillator Algebra and d-Orthogonal Polynomials

2021 ◽  
Author(s):  
Fethi Bouzeffour ◽  
Wissem Jedidi
Keyword(s):  
Orthogonal Polynomials ◽  
Oscillator Algebra

Automorphisms of the q-oscillator algebra and basic orthogonal polynomials

1993 ◽  
Vol 180 (6) ◽  
pp. 393-401 ◽  
Author(s):  
Roberto Floreanini ◽  
Luc Vinet
Keyword(s):  
Orthogonal Polynomials ◽  
Oscillator Algebra

scholarly journals Exactly and quasi-exactly solvable ‘discrete’ quantum mechanics

2011 ◽  
Vol 369 (1939) ◽  
pp. 1301-1318 ◽  
Author(s):  
Ryu Sasaki
Keyword(s):  
Quantum Mechanics ◽  
Orthogonal Polynomials ◽  
Essential Role ◽  
Dynamical Symmetry ◽  
Oscillator Algebra ◽  
Discrete Variable ◽  
Shape Invariance ◽  
One Dimensional ◽  
Exactly Solvable ◽  
Creation Operators

A brief introduction to discrete quantum mechanics is given together with the main results on various exactly solvable systems. Namely, the intertwining relations, shape invariance, Heisenberg operator solutions, annihilation/creation operators and dynamical symmetry algebras, including the q -oscillator algebra and the Askey–Wilson algebra. A simple recipe to construct exactly and quasi-exactly solvable (QES) Hamiltonians in one-dimensional ‘discrete’ quantum mechanics is presented. It reproduces all the known Hamiltonians whose eigenfunctions consist of the Askey scheme of hypergeometric orthogonal polynomials of a continuous or a discrete variable. Several new exactly and QES Hamiltonians are constructed. The sinusoidal coordinate plays an essential role.

scholarly journals More on the q-oscillator algebra and q-orthogonal polynomials

1995 ◽  
Vol 28 (10) ◽  
pp. L287-L293 ◽  
Author(s):  
R Floreanini ◽  
J LeTourneux ◽  
L Vinet
Keyword(s):  
Orthogonal Polynomials ◽  
Oscillator Algebra

scholarly journals q-Oscillator Algebra Andd-Orthogonal Polynomials

2013 ◽  
Vol 20 (4) ◽  
pp. 480-494 ◽  
Author(s):  
Fethi Bouzeffour ◽  
Ali Zagouhani
Keyword(s):  
Orthogonal Polynomials ◽  
Oscillator Algebra
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