Generating Function for a Linear Harmonic Oscillator

1972 ◽  
Vol 40 (3) ◽  
pp. 476-477
Author(s):  
Govind S. Khandelwal
Keyword(s):  
Harmonic Oscillator ◽  
Generating Function ◽  
Linear Harmonic Oscillator

Approach of the continuous q-Hermite polynomials to x-representation of q-oscillator algebra and its coherent states

2019 ◽  
Vol 17 (02) ◽  
pp. 2050021
Author(s):  
H. Fakhri ◽  
S. E. Mousavi Gharalari
Keyword(s):  
Harmonic Oscillator ◽  
Generating Function ◽  
Coherent States ◽  
Finite Interval ◽  
Hermite Polynomials ◽  
Oscillator Algebra ◽  
Text Representation ◽  
Ladder Operators ◽  
Recursion Relations ◽  
Wilson Operator

We use the recursion relations of the continuous [Formula: see text]-Hermite polynomials and obtain the [Formula: see text]-difference realizations of the ladder operators of a [Formula: see text]-oscillator algebra in terms of the Askey–Wilson operator. For [Formula: see text]-deformed coherent states associated with a disc in the radius [Formula: see text], we obtain a compact form in [Formula: see text]-representation by using the generating function of the continuous [Formula: see text]-Hermite polynomials, too. In this way, we obtain a [Formula: see text]-difference realization for the [Formula: see text]-oscillator algebra in the finite interval [Formula: see text] as a [Formula: see text]-generalization of known differential formalism with respect to [Formula: see text] in the interval [Formula: see text] of the simple harmonic oscillator.

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