Abstract:
It is shown that factorization of the difference equation for the Stieltjes–Wigert polynomials leads to a new explicit realization for the q-harmonic oscillator.
Citation:
N. M. Atakishiyev, S. K. Suslov, “A realization fo the q-harmonic oscillator”, TMF, 87:1 (1991), 154–156; Theoret. and Math. Phys., 87:1 (1991), 442–444
This publication is cited in the following 33 articles:
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E. I. Jafarov, “Description of the Bluffing Phenomenon in the Untrusted Seller–Buyer Relationship via the Wigner Function of the q-Deformed Quantum Harmonic Oscillator Model”, Studies in Microeconomics, 2024
Rafael Reno S. Cantuba, “Compactness property of Lie polynomials in the creation and annihilation operators of the q-oscillator”, Lett Math Phys, 110:10 (2020), 2639
H. Fakhri, S. E. Mousavi Gharalari, “Approach of the continuous q-Hermite polynomials to x-representation of q-oscillator algebra and its coherent states”, Int. J. Geom. Methods Mod. Phys., 17:02 (2020), 2050021
Rezan Sevinik Ad{\i}güzel, Sakina Alwhishi, Mehmet Turan, “On the limit of discrete q-Hermite I polynomials”, Communications Faculty Of Science University of Ankara Series A1Mathematics and Statistics, 2019, 2272
Rivera-Mocinos E., Sadurni E., “Inverse lattice design and its application to bent waveguides”, J. Phys. A-Math. Theor., 49:17 (2016), 175302
Galina Filipuk, Maciej Haneczok, 2013 15th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing, 2013, 97
J. S. Dehesa, P. Sánchez-Moreno, R. J. Yáñez, “Relative Fisher information of discrete classical orthogonal polynomials”, Journal of Difference Equations and Applications, 18:3 (2012), 489
R. Álvarez-Nodarse, “À la carte recurrence relations for continuous and discrete hypergeometric functions”, SeMA, 55:1 (2011), 41
R. S. Costas-Santos, F. Marcellán, “q-Classical Orthogonal Polynomials: A General Difference Calculus Approach”, Acta Appl Math, 111:1 (2010), 107
E I Jafarov, S Lievens, S M Nagiyev, J Van der Jeugt, “The Wigner function of aq-deformed harmonic oscillator model”, J. Phys. A: Math. Theor., 40:20 (2007), 5427
R. Álvarez-Nodarse, J.L. Cardoso, “Recurrence relations for discrete hypergeometric functions”, Journal of Difference Equations and Applications, 11:9 (2005), 829
R Álvarez-Nodarse, N M Atakishiyev, R S Costas-Santos, “Factorization of the hypergeometric-type difference equation on non-uniform lattices: dynamical algebra”, J. Phys. A: Math. Gen., 38:1 (2005), 153
R. Alvarez-Nodarse, M. K. Atakishiyeva, N. M. Atakishiyev, “On a q-extension of the linear harmonic oscillator with the continuous orthogonality property on ℝ”, Czech J Phys, 55:11 (2005), 1315
Andreas Ruffing, Julian Lorenz, Konstantin Ziegler, “Difference ladder operators for a harmonic Schrödinger oscillator using unitary linear lattices”, Journal of Computational and Applied Mathematics, 153:1-2 (2003), 395
G Bangerezako, M N Hounkonnou, “The factorization method for the general second-orderq-difference equation and the Laguerre Hahn polynomials on the generalq-lattice”, J. Phys. A: Math. Gen., 36:3 (2003), 765
R Álvarez-Nodarse, R S Costas-Santos, “Factorization method for difference equations of hypergeometric type on nonuniform lattices”, J. Phys. A: Math. Gen., 34:27 (2001), 5551
Metin Arik, Natig M Atakishiyev, Kurt Bernardo Wolf, “Quantum algebraic structures compatible with the harmonic oscillator Newton equation”, J. Phys. A: Math. Gen., 32:33 (1999), L371
R. Álvarez-Nodarse, J. Arvesú, “On theq-polynomials in the exponential latticex(s)=c1qs+c3”, Integral Transforms and Special Functions, 8:3-4 (1999), 299
R Álvarez-Nodarse, E Buendía, J S Dehesa, “The distribution of zeros of generalq-polynomials”, J. Phys. A: Math. Gen., 30:19 (1997), 6743
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