Nasser Saad Nasser Saad

Professor of Mathematics
School of Mathematical and Computational Sciences
University of Prince Edward Island
550 University Avenue
Charlottetown, PE
Canada C1A 4P3

Office: Cass 401
Telephone: (902) 566 0357
Fax: (902) 566 0466
E-mail: nsaad@upei.ca


Teaching assignment: 2018-2019

Math 2610: Linear Algebra I (2 sections).

Math 2620: Linear Algebra II.

Math 3920: Numerical Analysis.

Math 3010: Differential Equations.

Research Interests: Special Functions; Singular Potentials; Spectral Geometry; Eigenvalue Problems: Asymptotic Iteration Method; Heun's differential equations.
Publications
Professor Richard L. Hall's home page at Concordia University, Canada
Professor Yu. A. Brychkov at Dorodnicyn Computing Center of the Russian Academy of Sciences, Russia
Kalidas D. Sen, Professor of Chemistry, University of Hyderabad, India
Hakan Ciftci's home page at Gazi University, Turkey,
Professor Shi-Hai Dong's home page at National Polytechnic Institute, Mexico
Professor Hari M. Srivastava's home page at University of Victoria, Canada

Click here for my listings on the arXiv.

Click here for my listings on MathSciNet site.
Non-Refereed Publications
  1. Tables of the Appell Hypergeometric Functions F2
    Jonathan Murley and Nasser Saad [ps-pdf]
    arXiv:0809.5203v3 [math-ph, 2009].
  2. On the solvability of confluent Heun equation and associated orthogonal polynomials
    Nasser Saad [ps-pdf]
    arXiv:1509.00090v1 [math-ph, 2015].
Refereed Publications
  1. Exact normalized eigenfunctions for general deformed Hulthen potentials
    Richard L. Hall, Nasser Saad, and Kalidas Sen
    Journal of Mathematical Physics (In Press 2018).
  2. Analytical approximations to nonlinear oscillation of nanoelectro-mechanical resonators
    G. M. Ismail, M. Abul-Ez, N. M. Farea and Nasser Saad
    European Physical Journal Plus (In Press 2018).
  3. The d-dimensional softcore Coulomb potential and the generalized confluent Heun equation
    Richard L. Hall, Nasser Saad and Kyle R. Bryenton
    Journal of Mathematical Physics (In Press 2018).
  4. Some Results on the First Appell Matrix Function F1(A,B,B',C;z,w)
    H. Abd-Elmageed, M. Abdalla, M. Abul-Ez, and Nasser Saad
    Journal of Linear and Multilinear Algebra (In Press 2018).
  5. A note on the Generalized and Universal Associated Legendre Equations
    Keegan L. A. Kirk, Kyle R. Bryenton and Nasser Saad
    Communication in Theoretical Physics (In Press 2018).
  6. On some formulas for the Appell function F4(a,b; c, c';w, z)
    Yu. A. Brychkov and Nasser Saad
    Integral Transforms and Special Functions 28 (2017) 629 - 644.
  7. Exact and approximate solutions of Schroedinger's equation with hyperbolic double-well potentials
    Richard L. Hall and Nasser Saad[ps-pdf]
    European Physical Journal Plus 131 (2016) 277.
  8. Generalized 2D Laguerre polynomials and their quaternionic extensions
    Nasser Saad and K. Thirulogasanthar[ps-pdf]
    Journal of Computational and Applied Mathematics 308 (2016) 301 - 317.
  9. Solvable potentials with exceptional orthogonal polynomials
    Ash Arsenault, Sheldon Opps and Nasser Saad
    Annalen der Physik 528 (2016) 321 - 334.
  10. On some formulas for the Appell function F3(a, a',b, b'; c;w, z)
    Yu. A. Brychkov and Nasser Saad
    Integral Transforms and Special Functions 26 (2015) 910 - 923.
  11. 2D-Zernike polynomials and coherent state quantization of the unit disc
    K. Thirulogasanthar, Nasser Saad and G. Honnouvo [ps-pdf]
    Mathematical Physics, Analysis and Geometry 18 (2015) 13.
  12. Soft and hard confinement of a two-electron quantum system
    Richard Hall, Nasser Saad, and K. D. Sen [ps-pdf]
    European Physics Plus 129 (2014) 274.
  13. Schroedinger spectrum generated by the Cornell potential
    Richard Hall and Nasser Saad [ps-pdf]
    Central European Journal of Physics 13 (2015) 83 - 89.
  14. Casimir force in warped higher dimensional models (Survey)
    T.M. Aliev, Nasser Saad and Ismail Turan
    An International Journal of Applied and Computational Mathematics 13 (2014) 147 - 174.
  15. On W. Gordon's integral (1929) and related identities
    Nasser Saad [ps-pdf]
    Mathematica AETERNA (2014).
  16. Spectra generated by a confined softcore Coulomb potential
    Richard Hall and Nasser Saad [ps-pdf]
    Journal of Mathematical Physics (2014) - in press.
  17. Polynomial solutions for a class of second-order linear differential equations
    Nasser Saad, Richard Hall and Victoria Trenton [ps-pdf]
    Applied Mathematics and Computation 226 (2014) 615 - 634.
  18. On some formulas for the Appell function F2(a, b, b'; c,c';w, z)
    Yu. A. Brychkov and Nasser Saad
    Integral Transforms and Special Functions 25 (2014) 111 - 123.
  19. On some polynomial potentials in d-dimensions
    David Brandon, Nasser Saad and Shi-Hai Dong
    J. Math. Phys. 54 (2013) 082106.
  20. Quantum information entropies for an asymmetric trigonometric Rosen-Morse potential
    Guo-Hua Sun, Shi-Hai Dong, and Nasser Saad
    Ann. Physik, DOI:10.1002/andp.201300089, (2013).
  21. Exact and approximate solutions of Schroedinger's equation with decatic potentials [ps-pdf]
    David Brandon and Nasser Saad
    Central European Journal of Physics 11 (2013) 279-290.
  22. Exact and approximate solutions of Schroedinger's equation for a class of trigonometric potentials [ps-pdf]
    Hakan Ciftci, Richard L. Hall, and Nasser Saad
    Central European Journal of Physics 11 (2013) 37-48.
  23. On some formulas for the Appell function F1(a; b; b'; c;w; z)
    Yu. A. Brychkov and Nasser Saad
    Integral Transforms and Special Functions (2012) 793-802.
    Corrigendum: Integral Transforms and Special Functions (2012), DOI:10.1080/10652469.2012.668417.
  24. Discrete Spectra for Confined and Unconfined -a/r + br2 Potentials in d-Dimensions [ps-pdf]
    Richard L. Hall, Nasser Saad and K. D. Sen
    J. Math. Phys. 52 (2011) 092103.
  25. Study of the generalized quantum isotonic nonlinear oscillator potential [ps-pdf]
    Nasser Saad, Richard L. Hall, Hakan Ciftci and Ozlem Yesiltas
    Advances in Mathematical Physics Vol. 2011 (2011), Article ID 750168, 20 pages, doi:10.1155/2011/750168.
  26. On a modified beta function and some applications
    Ali Fatehi, Jonathan Murley and Nasser Saad
    Applied Mathematics and Computation 218 (2011) 1012-1018.
  27. Spectral characteristics for a spherically confiined -a/r + br2 potential [ps-pdf]
    Richard L. Hall, Nasser Saad and K. D. Sen
    J. Phys. A: Math. Theor. 44 (2011) 185307.
  28. Simple formula for computing the Hubbell radiation rectangular source integral
    Jonathan Murley and Nasser Saad
    Radiation Physics and Chemistry 80 (2011) 11-13.
  29. Generalized quantum isotonic nonlinear oscillator in d-dimensions[ps-pdf]
    Richard L. Hall, Nasser Saad, and Ozlem Yesilas
    J. Phys. A: Math. Theor. 43 (2010) 465304.
  30. Physical applications of second-order linear differential equations that admit polynomial solutions[ps-pdf]
    Hakan Ciftci, Richard L. Hall, Nasser Saad, Ebubekir Dogu
    J. Phys. A: Math. Theor. 43 (2010) 415206.
  31. Calculation of generalized Hubbell rectangular source integral [ps-pdf]
    Jonathan Murley and Nasser Saad
    Appl Radiat Isot. 69 (2010) 90-93.
  32. Soft-core Coulomb Potential and Heun's Differential Equation [ps-pdf]
    Richard L. Hall, Nasser Saad and K. D. Sen
    J. Math. Phys. 51 (2010) 022107.
  33. Energies and wave functions for a soft-core Coulomb potential [ps-pdf]
    Richard L. Hall, Nasser Saad, K. D. Sen, and Hakan Ciftci
    Phys. Rev. A 80, 032507 (2009).
  34. Simple Identity for Appell's Hypergeometric Function F2
    Amer Jajou and Nasser Saad
    Proceedings of a Conference on Analysis and Computational Mathematics, Notre Dame University, Lebanon (18-19 Sept. 2008). Editors: Friedemann Brock and Elias G. Saleeby, Research Publishing, Singapore (2009).
  35. Recursion Formulas for Appell's Hypergeometric Function F2 with Some Applications to Radiation Field Problems
    Sheldon B. Opps, Nasser Saad and H. M. Srivastava
    Applied Mathematics and Computation 207 (2009) 545-558.
  36. Solvable Systems of Linear Differential Equations [ps-pdf]
    Katherine M Robertson and Nasser Saad.
    Journal of Applied Mathematics and Computing: Volume 31, Issue 1 (2009), Page 475.
  37. Study of a confined Hydrogen-like atom by the Asymptotic Iteration Method [ps-pdf]
    Hakan Ciftci, Richard L. Hall, and Nasser Saad
    Int. J. Quant. Chem. 109, 931-937 (2009).
  38. The Casimir Force in Randall Sundrum Models with q+1 dimensions [ps-pdf]
    Mariana Frank, Nasser Saad and Ismail Turan
    Phys. Rev. D 78, 055014 (2008).
  39. Asymptotic Iteration Method for singular potentials [ps-pdf]
    Brodie Champion, Richard L. Hall, and Nasser Saad
    Int. J. Mod. Phys. A 23, (2008) 1405 - 1415.
  40. The Klein-Gordon equation with the Kratzer potential in d dimensions [ps-pdf]
    Nasser Saad, Richard L. Hall, and Hakan Ciftci
    Cent. Eur. J. Phys., 6 (2008) 717 - 729.
  41. The Klein-Gordon equation with a generalized Hulthen potential in D-dimensions [ps-pdf]
    Nasser Saad
    Phys. Scr. 76 (2007) 623-627.
  42. Eigenvalue bounds for polynomial central potentials in d dimensions [ps-pdf]
    Qutaibeh D. Katatbeh, Richard L. Hall and Nasser Saad
    J. Phys. A: Math. Theor. 40 (2007) 13431-13442.
  43. Solutions for certain classes of Riccati differential equation [ps-pdf]
    Nasser Saad, Richard L. Hall and Hakan Ciftci
    J. Phys. A: Math. Theor. 40 (2007) 10903-10914.
  44. Wave equation and dispersion relations for a compressible rotating fluid [ps-pdf]
    Jose Marin-Antuna, Richard L. Hall, and Nasser Saad
    Phys. Lett. A 362 (2007) 57 - 60.
  45. Criterion for polynomial solutions to a class of linear differential equation of second order [ps-pdf]
    Nasser Saad, Richard L. Hall and Hakan Ciftci
    J. Phys. A: Math. Gen. 39 (2006) 13445-13454.
  46. Sextic anharmonic oscillators and orthogonal polynomials [ps-pdf]
    Nasser Saad, Richard L. Hall and Hakan Ciftci
    J. Phys. A: Math. Gen. 39 (2006) 8477-8486.
  47. Study of a class of non-polynomial oscillator potentials [ps-pdf]
    Nasser Saad, Richard L. Hall and Hakan Ciftci
    J. Phys. A: Math. Gen. 39 (2006) 7745-7756.
  48. Iterative solutions to the Dirac equation [ps-pdf]
    Hakan Ciftci, Richard L. Hall, and Nasser Saad
    Phys. Rev. A, 72, 022101 (2005).
  49. Green's function for a Schreodinger operator and some related summation formulas [ps-pdf]
    Attila B. von Keviczky, Nasser Saad and Richard L. Hall
    J. Math. Phys., 46, 073512 (2005).
  50. Perturbation theory in a framework of iteration methods [ps-pdf]
    Hakan Ciftci, Richard L. Hall, and Nasser Saad
    Phys. Lett. A, 340, 388-396 (2005).
  51. Construction of exact solutions to eigenvalue problems by the asymptotic iteration method [ps-pdf]
    Hakan Ciftci, Richard L. Hall, and Nasser Saad
    J. Phys. A: Gen. Math. 38, 1147-1155 (2005).
  52. Study of Anharmonic Singular Potentials [ps-pdf]
    Nasser Saad, Richard L. Hall, and Qutaibeh D. Katatbeh
    J. Math. Phys. 46, 022104-022119 (2005).
  53. Some Reduction and Transformation Formulas for the Appell hypergeometric function F2
    Sheldon Opps, Nasser Saad, and H. M. Srivastava
    J. Math. Anal. Appl. 302, 184-199 (2005).
    Minor Corrections
  54. A basis for variational calculations in d dimensions [ps-pdf]
    Richard L. Hall, Qutaibeh D. Katatbeh, and Nasser Saad
    J. Phys. A: Math. Gen. 37, 11629-11644 (2004).
  55. Temporally stable coherent states for a free magnetic Schroedinger operator [ps-pdf]
    K. Thirulogasanthar, Nasser Saad, and Attila B von Keviczky
    J. Math. Phys., 45, 2694-2717 (2004).
  56. Friedrichs Extensions of Schroedinger Operators with Singular Potentials [ps-pdf]
    Attila B von Keviczky, Nasser Saad, and Richard L. Hall
    J. Math. Anal. Appl., 292, 274-293 (2004).
  57. Coherent States associated with the wavefunctions and the spectrum of the isotonic oscillator [ps-pdf]
    K. Thirulogasanthar and Nasser Saad
    J. Phys. A: Math. Gen. 37, 4567-4577 (2004).
  58. Perturbation expansions for a class of singular potentials [ps-pdf]
    Nasser Saad, Richard L. Hall and Attila B von Keviczky
    J. Math. Phys. 44, 5021-5041 (2003).
  59. Asymptotic iteration method for eigenvalue problems [ps-pdf]
    Hakan Ciftci, Richard L. Hall, and Nasser Saad
    J. Phys. A 36, 11807-11816 (2003) .
  60. Integrals containing confluent hypergeometric functions with applications to perturbed singular potentials [ps-pdf]
    Nasser Saad, Richard L. Hall and Attila B von Keviczky
    J. Phys. A.: Gen. Math. 36, 7771-7788 (2003)
  61. Energy bounds for a class of singular potentials and some related series [ps-pdf]
    Nasser Saad, Richard L. Hall and Attila B von Keviczky,
    J. Phys. A.: Gen. Math. 36, 487-498 (2003)
  62. Closed-form sums for some perturbation series involving hypergeometric functions [ps-pdf]
    Nasser Saad and Richard L. Hall
    J. Phys. A.: Gen. Math. 35, 4105-4123 (2002)
  63. Spiked harmonic oscillators [ps-pdf]
    Richard L. Hall, Nasser Saad, and Attila B von Keviczky
    J. Math. Phys. 43, 94-112 (2002).
  64. Closed-form sums for some perturbation series involving associated Laguerre polynomials [ps-pdf]
    Richard L. Hall, Nasser Saad, and Attila B von Keviczky
    J. Phys. A: Math. Gen. 34, 11287-11300 (2001).
  65. Generalized spiked harmonic oscillator [ps-pdf]
    Richard L. Hall, Nasser Saad, and Attila B von Keviczky
    J.Phys. A: Math. Gen. 34, 1169-1179 (2001).
  66. Perturbation expansions for the spiked harmonic oscillator and related series involving the gamma function [ps pdf]
    Richard L. Hall and Nasser Saad
    J.Phys. A: Math. Gen. 33, 5531-5537 (2000).
  67. Variational analysis for a generalized spiked harmonic oscillator [ps pdf]
    Richard L. Hall and Nasser Saad
    J. Phys. A: Math. Gen. 33, 569-578 (2000).
  68. Eigenvalue bounds for a class of singular potentials in N-dimensions [pdf]
    Richard L. Hall and Nasser Saad
    J. Phys. A: Math. Gen. 32, 133-138 (1999).
  69. Matrix elements for a generalized spiked harmonic oscillator [pdf]
    Richard L. Hall, Nasser Saad, and Attila B. von Keviczky
    J. Math. Phys. 39, 6345-6352 (1998)
  70. Smooth transformations of Kratzer's potential in N dimensions
    Richard L. Hall and Nasser Saad
    J. Chem. Phys. 109, 2983-2986 (1998).
  71. Eigenvalue bounds for a class of singular potentials
    Richard L. Hall and Nasser Saad
    J. Phys. A: Math. Gen. 31, 963-967 (1998).
  72. Eigenvalue comparisons for quantum systems in a box
    Richard L. Hall and Nasser Saad
    Phys. Lett. A 237, 107-112 (1998)
  73. Bounds on Schrödinger eigenvalues for polynomial potentials in N dimensions
    Richard L. Hall and Nasser Saad
    J. Math. Phys. 38, 4909-4913 (1997)
  74. Eigenvalue bounds for transformations of solvable potentials,
    Richard L. Hall and Nasser Saad
    J. Phys. A: Math. Gen. 29, 2127-2137 (1996).
  75. The quantum-mechanical box effect [pdf]
    Richard L. Hall and Nasser Saad
    J. Phys. A. Math. Gen. 29, 2127-2137 (1996).
  76. Energy bounds for the spiked harmonic oscillator
    Richard L. Hall and Nassser Saad
    Can. J. Phys. 73 , 493-496 (1995).
To my teachers:
Attila Bela von Keviczky (1941 - 2008) Eulogy
Syed Twareque Ali (1942 - 2016) OBITUARY