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