Mots-clés : Bessel polynomial.
@article{TMF_2021_206_1_a4,
author = {A. D. Alhaidari},
title = {Exponentially confining potential well},
journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
pages = {97--111},
year = {2021},
volume = {206},
number = {1},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TMF_2021_206_1_a4/}
}
A. D. Alhaidari. Exponentially confining potential well. Teoretičeskaâ i matematičeskaâ fizika, Tome 206 (2021) no. 1, pp. 97-111. http://geodesic.mathdoc.fr/item/TMF_2021_206_1_a4/
[1] N. Zettili, Quantum Mechanics: Concepts and Applications, Wiley, New York, 2009 | MR
[2] P. L. Ferreira, J. A. Helayel, N. Zagury, “A linear-potential model for quark confinement”, Il Nuovo Cimento A, 55 (1980), 215–226 | DOI
[3] A. Nakamura, T. Saito, “QCD color interactions between two quarks”, Phys. Lett. B, 621:1–2 (2005), 171–175, arXiv: hep-lat/0512043 | DOI
[4] F. Cooper, A. Khare, U. Sukhatme, Supersymmetry in Quantum Mechanics, World Sci., Singapore, 2004 | MR
[5] M. Bander, C. Itzykson, “Group theory and the hydrogen atom (I)”, Rev. Modern Phys., 38:2 (1966), 330–345 | DOI | MR
[6] Y. Alhassid, F. Iachello, F. Gürsey, “Group theory of the Morse oscillator”, Chem. Phys. Lett., 99:1 (1983), 27–30 | DOI
[7] L. Infeld, T. E. Hull, “The factorization method”, Rev. Modern Phys., 23:1 (1951), 21–68 | DOI | MR
[8] H. Ciftci, R. L. Hall, N. Saad, “Construction of exact solutions to eigenvalue problems by the asymptotic iteration method”, J. Phys. A: Math. Gen., 38:5 (2005), 1147–1155 | DOI | MR | Zbl
[9] R. De, R. Dutt, U. Sukhatme, “Mapping of shape invariant potentials under point canonical transformations”, J. Phys. A: Math. Gen., 25:13 (1992), L843–L850 | DOI | MR
[10] R. Feinman, A. Khibs, Kvantovaya mekhanika i integraly no traektoriyam, Mir, M., 1968 | MR
[11] A. F. Nikiforov, V. B. Uvarov, Spetsialnye funktsii matematicheskoi fiziki, Nauka, M., 1984 | MR | Zbl
[12] A. D. Alhaidari, H. Bahlouli, “Tridiagonal representation approach in quantum mechanics”, Phys. Scripta, 94:12 (2019), 125206, arXiv: 1903.00322 | DOI
[13] A. G. Ushveridze, Quasi-Exactly Solvable Models in Quantum Mechanics, Institute of Physics Publishing, Bristol, 1994 | MR
[14] T. S. Chihara, An introduction to orthogonal polynomials, Mathematics and its Applications, 13, Gordon and Breach, New York, London, Paris, 1978 | MR
[15] G. Szegő, Orthogonal Polynomials, AMS, Providence, RI, 1975 | MR
[16] A. D. Alhaidari, M. E. H. Ismail, “Quantum mechanics without potential function”, J. Math. Phys., 56:7 (2015), 072107, 19 pp. | DOI | MR
[17] A. D. Alhaidari, “Representation of the quantum mechanical wavefunction by orthogonal polynomials in the energy and physical parameters”, Commun. Theor. Phys., 72:1 (2020), 015104, 15 pp. | DOI | MR
[18] R. Koekoek, P. A. Lesky, R. F. Swarttouw, Hypergeometric Orthogonal Polynomials and Their $q$-Analogues, Springer Monographs in Mathematics, Springer, Berlin, 2010 | DOI | MR
[19] F. W. J. Olver, A. B. Olde Daalhuis, D. W. Lozier, B. I. Schneider, R. F. Boisvert, C. W. Clark, B. R. Miller, B. V. Saunders (eds.), NIST Digital Library of Mathematical Functions http://dlmf.nist.gov
[20] Wolfram Koepf, CAOP: Computer Algebra Orthogonal Polynomials,\par, http://www.caop.org/
[21] W. Koepf, D. Schmersau, “Recurrence equations and their classical orthogonal polynomial solutions”, Appl. Math. Comput., 128:2–3 (2002), 303–327 | DOI | MR
[22] P. C. Ojha, “$\rm{SO}(2,1)$ Lie algebra, the Jacobi matrix and the scattering states of the Morse oscillator”, J. Phys. A: Math. Gen., 21:4 (1988), 875–883 | DOI | MR
[23] A. D. Alhaidari, “Open problem in orthogonal polynomials”, Rep. Math. Phys., 84:3 (2019), 393–405 | DOI | MR
[24] A. D. Alhaidari, “Orthogonal polynomials derived from the tridiagonal representation approach”, J. Math. Phys., 59:1 (2018), 013503, 8 pp., arXiv: 1703.04039 | DOI | MR
[25] W. Van Assche, “Solution of an open problem about two families of orthogonal polynomials”, SIGMA, 15 (2019), 005, 6 pp. | DOI | MR
[26] A. D. Alhaidari, “Reconstructing the potential function in a formulation of quantum mechanics based on orthogonal polynomials”, Commun. Theor. Phys., 68:6 (2017), 711–728 | DOI | MR
[27] G. H. Golub, G. Meurant, Matrices, Moments and Quadrature with Applications, Princeton Series in Applied Mathematics, 30, Princeton Univ. Press, Princeton, 2010 | MR
[28] W. Gautschi, Orthogonal Polynomials: Computation and Approximation, Numerical Mathematics and Scientific Computation, Oxford Univ. Press, Oxford, 2004 | MR
[29] P. J. Davis, P. Rabinowitz, Methods of Numerical Integration, Academic Press, Orlando, FL, 1984 | MR