Các đa thức Romanovski trong các bài toán vật lý chọn lọc
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Tài liệu tham khảo
E.J. Routh: “On some properties of certain solutions of a differential equation of second order”, Proc. London Math. Soc., Vol. 16, (1884), pp. 245–261.
V. Romanovski: “Sur quelques classes nouvelles de polynomes orthogonaux”, C. R. Acad. Sci. Paris, Vol. 188, (1929), pp. 1023–1025.
A.F. Nikiforov and V.B. Uvarov: Special Functions of Mathematical Physics, Birkhäuser Verlag, Basel, 1988.
P.A. Lesky: “Endliche und unendliche Systeme von kontinuierlichen klassischen Orthogonalpolynomen”, Z. Angew. Math. Mech., Vol. 76, (1996), pp. 181–184.
H.J. Weber: “Connections between real polynomial solutions of hypergeometrictype differential equations with Rodrigues formula”, Centr. Eur. J. Math., Vol. 5(2), (2007), pp. 415–427.
D.E. Alvarez-Castillo and M. Kirchbach: “Exact spectrum and wave functions of the hyperbolic Scarf potential in terms of finite Romanovski polynomials”, E-Print Archive: quant-ph/0603122.
C.B. Compean and M. Kirchbach: “The trigonometric Rosen-Morse potential in supersymmetric quantum mechanics and its exact solutions”, J. Phys. A: Math. Gen., Vol. 39, (2006), pp. 547–557 and refs. therein.
Wen-Chao Qiang: “Bound States of Klein-Gordon equation for ring-shaped harmonic oscillator scalar and vector potentials”, Chin. Phys., Vol. 12, (2003), pp. 136–139; Wen-Chao Qiang and Shi-Hai Dong: “SUSYQM and SWKB Approaches to the Relativistic Equations with Hyperbolic Potential V0tangh2(r/d),” Physica Scripta, Vol. 72, (2005), pp. 127–131.
R. Dutt, A. Gangopadhyaya and U.P. Sukhatme: “Non-Central Potentials and Spherical Harmonics Using Supersymmetry and Shape Invariance”, Am. J. Phys., Vol. 65, (1997), pp. 400–403; E-Print Archive: hep-th / 9611087.
N. Cotfas: “Systems of orthogonal polynomials defined by hypergeometric type equations with application to quantum mechanics”, Centr. Eur. J. Phys., Vol. 2, (2004), pp. 456–466; N. Cotfas: “Shape invariant hypergeometric type operators with application to quantum mechanics”, E-Print Archive: math-ph/0603032.
M.E.H. Ismail: Classical and Quantum Orthogonal Polynomials in One Variable, Cambridge Univ. Press, 2005.
H.L. Krall and O. Fink: “A New Class of Orthogonal Polynomials: The Bessel Polynomials”, Trans. Amer. Math. Soc., Vol. 65, (1948), pp. 100–115.
A. Zarzo-Altarejos: “Differential Equations of the Hypergeometric Type”, Thesis (Ph.D.), Faculty of Science, University of Granada, 1995 (in Spanish).
R. Askey: “Beta integrals and the associated orthogonal polynomials”, In: Number Theory, Vol. 1395 of Lecture Notes in Math., Madras, Springer, Berlin, 1987, pp. 84–121.
C.B. Compean and M. Kirchbach: “Angular Momentum Dependent Quark Potential of QCD Traits and Dynamical O(4) Symmetry”, Bled Workshops in Physics, Vol. 7, (2006), pp. 7–19, E-Print Archive: quant-ph/0610001.
P. Dennery and A. Krzywicki: Mathematics for Physicists, Dover, New York, 1996.
M. Abramowitz and I.A. Stegun: Handbook of Mathematical Functions with Formulas, Graphs and Mathematical Tables, 2nd ed., Dover, New York, 1972.
G.B. Arfken and H.J. Weber: Mathematical Methods for Physicists, 6th ed., Elsevier-Academic Press, Amsterdam, 2005.
A.B.J. Kuijlaars, A. Martínez-Finkelshtein and R. Orive: “Orthogonality of Jacobi Polynomials with General Parameters”, Electronic Transactions on Numerical Analysis, Vol. 19, (2003), pp. 1–17.
W. Greiner and B. Müller: Quantum Mechanics: Symmetries, 2nd rev. ed., Springer, Berlin-Heidelberg, 2004; G.F. Torres del Castillo and J.L. Calvario Acócal: “On the Dynamical Symmetry of the Quantum Kepler Problem”, Rev. Mex. Fis., Vol. 44(4), (1998), pp. 344–352.
V.C. Aguilera-Navarro, E. Ley-Koo and S. Mateos-Cortés: “Vibrational-Rotational Analysis of the Hulthen Potential Using Hydrogenic Eigenfunction Bases”, Rev. Mex. Fis., Vol. 44, (1998), pp. 413–419.
F. Iachello and R.D. Levine: Algebraic Theory of Molecules, Oxford Univ. Press, New York, 1992.
P.M. Morse and H. Feshbach: Methods of Theoretical Physics, Part I, McGraw-Hill Book Company, Inc., New York, 1953.
C. V. Sukumar: “Supersymmetric Quantum Mechanics of One-Dimensional Systems”, J. Phys. A: Math. Gen., Vol. 18, (1985), pp. 2917–2936; C.V. Sukumar: “Supersymemtric Quantum Mechanics and Its Applications”, In: R. Bijker et al. (Eds.): Supersymmetries in physics and applications, AIP Proc., Vol. 744, New York, 2005, pp. 166–235.
F. Cooper, A. Khare and U.P. Sukhatme: Supersymmetry in Quantum Mechanics, World Scientific, Singapore, 2001.
G. Lévai: “A Search for Shape Invariant Solvable Potentials”, J. Phys. A: Math. Gen., Vol. 22, (1989), pp. 689–702.
B. Bagchi and R. Roychoudhury: “A new PT-symmetric complex hamiltonian with a real spectrum”, J. Phys. A: Math. Gen., Vol. 33, (2000), L1–L3.
W. Koepf and M. Masjed-Jamei: “A Generic Polynomial Solution for the Differential Equation of Hypergeometric Type and Six Sequences of Orthogonal Polynomials”, Integral Transforms and Special Functions, Vol. 17, (2006), pp. 559–576; M. Masjed-Jamei: “Classical Orthogonal Polynomials with Weight Function ((ax + b)2 + (cx + d)2)−p exp(q) arctan $$\tfrac{{ax + b}}{{cx + d}}x \in ( - \infty , + \infty )$$ and Generalization of T and F Distributions”, Integral Transforms and Special Functions, Vol. 15, (2002), pp. 137–153.
Particle Data Group, S. Eidelman et al.: “Review of Particle Physics”, Phys. Lett. B, Vol. 592, (2004), pp. 1–1109.
M. Kirchbach: “On the parity degeneracy of baryons”, Mod. Phys. Lett. A, Vol. 12, (1997), pp. 2373–2386.
M. Kirchbach, M. Moshinsky and Yu.F. Smirnov: “Baryons in O(4) and vibron model”, Phys. Rev. D, Vol. 64, (2001), art. 114005.
E.P. Wigner: “Characteristic Vectors of Bordered Matrices with Infinite Dimensions”, Ann. Math., Vol. 62, (1955), pp. 548–564.
N.S. Witte and P.J. Forrester: “Gap probabilities in the finite and scaled Caushy Random Matrix Ensambles”, Nonlinearity, Vol. 13, (2000), pp. 1965–1986; P.J. Forrester: Random Matrices in Log Gases, http://www.ms.unimelb.edu.au/~mathpjf/mathpjf.html (book in preparation).