Exponentially confining potential well
Teoretičeskaâ i matematičeskaâ fizika, Tome 206 (2021) no. 1, pp. 97-111 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

We introduce an exponentially confining potential well that can be used as a model to describe the structure of a strongly localized system. We obtain an approximate partial solution of the Schrödinger equation with this potential well where we find the lowest energy spectrum and the corresponding wavefunctions. We use the tridiagonal representation approach as the method for obtaining the solution as a finite series of square-integrable functions written in terms of Bessel polynomials.
Keywords: exponential potential, tridiagonal representation approach
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/}
}
TY  - JOUR
AU  - A. D. Alhaidari
TI  - Exponentially confining potential well
JO  - Teoretičeskaâ i matematičeskaâ fizika
PY  - 2021
SP  - 97
EP  - 111
VL  - 206
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/TMF_2021_206_1_a4/
LA  - ru
ID  - TMF_2021_206_1_a4
ER  - 
%0 Journal Article
%A A. D. Alhaidari
%T Exponentially confining potential well
%J Teoretičeskaâ i matematičeskaâ fizika
%D 2021
%P 97-111
%V 206
%N 1
%U http://geodesic.mathdoc.fr/item/TMF_2021_206_1_a4/
%G ru
%F 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