Hamiltonian%20structure
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1: 32.6 Hamiltonian Structure
§32.6 Hamiltonian Structure
… ►For Hamiltonian structure for see Jimbo and Miwa (1981), Okamoto (1986); also Forrester and Witte (2001). ►For Hamiltonian structure for see Jimbo and Miwa (1981), Okamoto (1987b); also Forrester and Witte (2002). ►For Hamiltonian structure for see Jimbo and Miwa (1981) and Okamoto (1987a); also Forrester and Witte (2004).2: 29.19 Physical Applications
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§29.19(i) Lamé Functions
… ►Brack et al. (2001) shows that Lamé functions occur at bifurcations in chaotic Hamiltonian systems. …3: Bibliography
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Exact linearization of a Painlevé transcendent.
Phys. Rev. Lett. 38 (20), pp. 1103–1106.
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On the degrees of irreducible factors of higher order Bernoulli polynomials.
Acta Arith. 62 (4), pp. 329–342.
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Study of nuclear structure by electromagnetic excitation with accelerated ions.
Rev. Mod. Phys. 28, pp. 432–542.
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Repeated integrals and derivatives of Bessel functions.
SIAM J. Math. Anal. 20 (1), pp. 169–175.
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The Riemann Hypothesis and the Hamiltonian of a Quantum Mechanical System.
In Number Theory and Dynamical Systems (York, 1987), M. M. Dodson and J. A. G. Vickers (Eds.),
London Math. Soc. Lecture Note Ser., Vol. 134, pp. 153–172.
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4: 18.39 Applications in the Physical Sciences
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►The fundamental quantum Schrödinger operator, also called the Hamiltonian, , is a second order differential operator of the form
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►Physical scientists use the of Bohr as, to th and st order, it describes the structure and organization of the Periodic Table of the Chemical Elements of which the Hydrogen atom is only the first.
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►Derivations of (18.39.42) appear in Bethe and Salpeter (1957, pp. 12–20), and Pauling and Wilson (1985, Chapter V and Appendix VII), where the derivations are based on (18.39.36), and is also the notation of Piela (2014, §4.7), typifying the common use of the associated Coulomb–Laguerre polynomials in theoretical quantum chemistry.
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►A relativistic treatment becoming necessary as becomes large as corrections to the non-relativistic Schrödinger picture are of approximate order , being the dimensionless fine structure constant , where is the speed of light.
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5: Bibliography Y
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-squared discretizations of the continuum: Radial kinetic energy and the Coulomb Hamiltonian.
Phys. Rev. A 11 (4), pp. 1144–1156.
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6: 20 Theta Functions
Chapter 20 Theta Functions
…7: Bibliography B
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Pionic atoms.
Annual Review of Nuclear and Particle Science 20, pp. 467–508.
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Coulomb functions (negative energies).
Comput. Phys. Comm. 20 (3), pp. 447–458.
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Some solutions of the problem of forced convection.
Philos. Mag. Series 7 20, pp. 322–343.
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Integrable Hamiltonian systems and the Painlevé property.
Phys. Rev. A (3) 25 (3), pp. 1257–1264.
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Occurrence of periodic Lamé functions at bifurcations in chaotic Hamiltonian systems.
J. Phys. A 34 (40), pp. 8199–8220.
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8: 34.12 Physical Applications
§34.12 Physical Applications
… ►For applications in nuclear structure, see de-Shalit and Talmi (1963); in atomic spectroscopy, see Biedenharn and van Dam (1965, pp. 134–200), Judd (1998), Sobelman (1992, Chapter 4), Shore and Menzel (1968, pp. 268–303), and Wigner (1959); in molecular spectroscopy and chemical reactions, see Burshtein and Temkin (1994, Chapter 5), and Judd (1975). …9: Bibliography N
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On an integral transform involving a class of Mathieu functions.
SIAM J. Math. Anal. 20 (6), pp. 1500–1513.
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Reduction and evaluation of elliptic integrals.
Math. Comp. 20 (94), pp. 223–231.
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A table of integrals of the error functions.
J. Res. Nat. Bur. Standards Sect B. 73B, pp. 1–20.
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Natural Focusing and Fine Structure of Light: Caustics and Wave Dislocations.
Institute of Physics Publishing, Bristol.
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10: Bibliography K
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Determinant structure of the rational solutions for the Painlevé II equation.
J. Math. Phys. 37 (9), pp. 4693–4704.
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Determinant structure of the rational solutions for the Painlevé IV equation.
J. Phys. A 31 (10), pp. 2431–2446.
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Algorithm 737: INTLIB: A portable Fortran 77 interval standard-function library.
ACM Trans. Math. Software 20 (4), pp. 447–459.
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Methods of computing the Riemann zeta-function and some generalizations of it.
USSR Comput. Math. and Math. Phys. 20 (6), pp. 212–230.
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The structure relation for Askey-Wilson polynomials.
J. Comput. Appl. Math. 207 (2), pp. 214–226.
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