Hypercomplex Fock states for discrete electromagnetic Schrödinger operators: A Bayesian probability perspective

Applied Mathematics and Computation - Tập 315 - Trang 531-548 - 2017
N. Faustino1
1CMCC, Universidade Federal do ABC, 09210-580 Santo André, SP, Brazil

Tài liệu tham khảo

Aptekarev, 2015, On 2d discrete Schrödinger operators associated with multiple orthogonal polynomials, J. Phys. A: Math. Theor., 48, 16 Bender, 2005, Introduction to PT-symmetric quantum theory, Contemp. Phys., 46, 277, 10.1080/00107500072632 Bender, 2006, Equivalence of a complex PT-symmetric quartic Hamiltonian and a Hermitian quartic Hamiltonian with an anomaly, Phys. Rev. D, 74, 025016, 10.1103/PhysRevD.74.025016 Bender, 2008, Exact isospectral pairs of PT symmetric Hamiltonians, J. Phys. A: Math. Theor., 41, 244005, 10.1088/1751-8113/41/24/244005 Bender, 2010, Probability density in the complex plane, Anna. Phys., 325, 2332, 10.1016/j.aop.2010.02.011 Campos, 2011, A finite-sum representation for solutions for the Jacobi operator, J. Differ. Equ. Appl., 17, 567, 10.1080/10236190903158990 Caves, 2002, Quantum probabilities as Bayesian probabilities, Phys. Rev. A, 65, 022305, 10.1103/PhysRevA.65.022305 Chakrabarti, 2010, Quantum communication through a spin chain with interaction determined by a Jacobi matrix, J. Phys. A: Math. Theor., 43, 085302, 10.1088/1751-8113/43/8/085302 Constales, 2011, Fock spaces, Landau operators and the time-harmonic Maxwell equations, J. Phys. A: Math. Theor., 44, 135303, 10.1088/1751-8113/44/13/135303 Cooper, 1995, Supersymmetry and quantum mechanics, Phys. Rep., 251, 267, 10.1016/0370-1573(94)00080-M Dirac, 1942, Bakerian lecture. The physical interpretation of quantum mechanics, Proc. R. Soc. Lond. Ser. A Math. Phys. Sci., 180, 1 Erdélyi, 1953, Higher transcendental functions Faustino, 2011, (Discrete) Almansi type decompositions: an umbral calculus framework based on osp(1|2) symmetries, Math. Methods Appl. Sci., 34, 1961, 10.1002/mma.1498 Faustino, 2013, Special functions of hypercomplex variable on the lattice based on SU(1, 1), SIGMA, 9, 18 Faustino, 2014, Classes of hypercomplex polynomials of discrete variable based on the quasi-monomiality principle, Appl. Math. Comput., 247, 607, 10.1016/j.amc.2014.09.027 Floreanini, 1993, Quantum mechanics and polynomials of a discrete variable, Ann. Phys., 226, 331, 10.1006/aphy.1993.1072 Fock, 1932, Konfiguration raum und zweite quantelung, Z. Phys., 75, 622, 10.1007/BF01344458 Gesztesy, 1996, Commutation methods for Jacobi operators, J. Differ. Equ., 128, 252, 10.1006/jdeq.1996.0095 Gilbert, 1991, 26 Kilbas, 2002, On the generalized Wright function, Fract. Calc. Appl. Anal., 5, 437 Macdonald, 1996, Affine Hecke algebras and orthogonal polynomials, Sémin. Bourbaki, 37, 189 Macdonald, 2000, Orthogonal polynomials associated with root systems, Sémin. Lothar. Comb., 45, 311 Mathai, 2009 Miki, 2012, Quantum-state transfer in a two-dimensional regular spin lattice of triangular shape, Phys. Rev. A, 85, 062306, 10.1103/PhysRevA.85.062306 Montvay, 1994 Mouayn, 2014, Husimi’s q-function of the isotonic oscillator in a generalized negative binomial states representation, Math. Phys. Anal. Geom., 17, 289, 10.1007/s11040-014-9156-3 Odake, 2005, Shape invariant potentials in ‘discrete quantum mechanics’, J. Nonlinear Math. Phys., 12, 507, 10.2991/jnmp.2005.12.s1.41 Odake, 2009, Crum’s theorem for ‘discrete’ quantum mechanics, Prog. Theor. Phys., 122, 1067, 10.1143/PTP.122.1067 Odake, 2009, Infinitely many shape invariant discrete quantum mechanical systems and new exceptional orthogonal polynomials related to the Wilson and Askey–Wilson polynomials, Phys. Lett. B, 682, 130, 10.1016/j.physletb.2009.10.078 Odake, 2010, Unified theory of exactly and quasiexactly solvable ‘discrete’ quantum mechanics. I. Formalism, J. Math. Phys., 51, 083502, 10.1063/1.3458866 Rabinovich, 2009, Essential spectra and exponential estimates of eigenfunctions of lattice operators of quantum mechanics., J. Phys. A: Math. Theor., 42, 385207, 10.1088/1751-8113/42/38/385207 Ruijsenaars, 1995, Action-angle maps and scattering theory for some finite-dimensional integrable systems III. Sutherland type systems and their duals, Publ. Res. Inst. Math. Sci., 31, 247, 10.2977/prims/1195164440 Ruijsenaars, 2002, Factorized weight functions vs. factorized scattering, Commun. Math. Phys., 228, 467, 10.1007/s002200200662 Spiridonov, 1993, Difference Schrödinger operators with linear and exponential discrete spectra, Lett. Math. Phys., 29, 63, 10.1007/BF00760860 Simon, 1998, The classical moment problem as a self-adjoint finite difference operator, Adv. Math., 137, 82, 10.1006/aima.1998.1728 Teschl, 2000, Jacobi Operators and Completely Integrable Nonlinear Lattices, Am. Math. Soc. Stoilova, 2011, An exactly solvable spin chain related to Hahn polynomials, SIGMA, 7, 13 Van Diejen, 2005, Scattering theory of discrete (pseudo) Laplacians on a Weyl chamber, Am. J. Math., 127, 421, 10.1353/ajm.2005.0012 van Diejen, 2015, Difference equation for the Heckman–Opdam hypergeometric function and its confluent Whittaker limit, Adv. Math., 285, 1225, 10.1016/j.aim.2015.08.018 van Diejen, 2015, Spectrum and eigenfunctions of the lattice hyperbolic Ruijsenaars–Schneider system with exponential morse term, Ann. Henri Poincaré, 1