scholarly journals Shape Invariant Potential Formalism for Photon-Added Coherent State Construction

2018 ◽  
pp. 393-421
Author(s):  
Komi Sodoga ◽  
Isiaka Aremua ◽  
Mahouton Norbert Hounkonnou
Keyword(s):  
Coherent State ◽  
Shape Invariant ◽  
State Construction ◽  
Invariant Potential ◽  
Potential Formalism

scholarly journals Shape invariant rational extensions and potentials related to exceptional polynomials

2015 ◽  
Vol 30 (24) ◽  
pp. 1550146 ◽  
Author(s):  
S. Sree Ranjani ◽  
R. Sandhya ◽  
A. K. Kapoor
Keyword(s):  
Shape Invariant ◽  
Invariant Potential ◽  
Exceptional Polynomials ◽  
Infinite Sets ◽  
Infinite Set ◽  
Explicit Expressions

In this paper, we show that an attempt to construct shape invariant extensions of a known shape invariant potential leads to, apart from a shift by a constant, the well known technique of isospectral shift deformation. Using this, we construct infinite sets of generalized potentials with [Formula: see text] exceptional polynomials as solutions. The method is simple and transparent and is elucidated using the radial oscillator and the trigonometric Pöschl–Teller potentials. For the case of radial oscillator, in addition to the known rational extensions, we construct two infinite sets of rational extensions, which seem to be less studied. Explicit expressions of the generalized infinite set of potentials and the corresponding solutions are presented. For the trigonometric Pöschl–Teller potential, our analysis points to the possibility of several rational extensions beyond those known in literature.

A New Type of Shape-Invariant Potential

1998 ◽  
Vol 30 (2) ◽  
pp. 305-308 ◽  
Author(s):  
Jia Chunsheng ◽  
Wang Xiaoguo ◽  
Yang Qiubo ◽  
He Su ◽  
Li Hao
Keyword(s):  
Shape Invariant ◽  
Invariant Potential ◽  
New Type

scholarly journals Shape-invariant potentials and an associated coherent state

1993 ◽  
Vol 180 (4-5) ◽  
pp. 308-313 ◽  
Author(s):  
Takahiro Fukui ◽  
N. Aizawa
Keyword(s):  
Coherent State ◽  
Shape Invariant
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