Results 31 to 40 of about 1,201 (100)
Discrete Quantum Mechanics [PDF]
, 2011 A comprehensive review of the discrete quantum mechanics with the pure imaginary shifts and the real shifts is presented in parallel with the corresponding results in the ordinary quantum mechanics.
Odake, Satoru, Sasaki, Ryu
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Shape Invariant Potentials in "Discrete Quantum Mechanics" [PDF]
, 2004 Shape invariance is an important ingredient of many exactly solvable quantum mechanics. Several examples of shape invariant ``discrete quantum mechanical systems" are introduced and discussed in some detail.
Odake, S., Sasaki, R.
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The generalized Koebe function [PDF]
Проблемы анализа, 2010 We observe that the extremal function for |a 3| within the class U' α (see Starkov [1]) has as well the property that max|A 4|>4.15, if α=2. The problem is equivalent to the global estimate for Meixner-Pollaczek polynomials P 1 3(x;θ).
Naraniecka I., Szynal J., Tatarczak A.
doaj
The asymptotics of the mittag-leffler polynomials [PDF]
, 2012 We investigate the asymptotic behaviour of the Mittag-Leffler polynomials Gn(z) for large n and z, where z is a complex variable satisfying 0 arg z 12 π .
Paris, Richard B.
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Bethe Ansatz Solutions to Quasi Exactly Solvable Difference Equations
Symmetry, Integrability and Geometry: Methods and Applications, 2009 Bethe ansatz formulation is presented for several explicit examples of quasi exactly solvable difference equations of one degree of freedom which are introduced recently by one of the present authors.
Ryu Sasaki, Wen-Li Yang, Yao-Zhong Zhang
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Meixner polynomials of the second kind and quantum algebras representing su(1,1)
, 2009 We show how Viennot's combinatorial theory of orthogonal polynomials may be used to generalize some recent results of Sukumar and Hodges on the matrix entries in powers of certain operators in a representation of su(1,1).
Chihara T. S. +3 more
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Exactly solvable `discrete' quantum mechanics; shape invariance, Heisenberg solutions, annihilation-creation operators and coherent states [PDF]
, 2008 Various examples of exactly solvable `discrete' quantum mechanics are explored explicitly with emphasis on shape invariance, Heisenberg operator solutions, annihilation-creation operators, the dynamical symmetry algebras and coherent states.
Odake, Satoru, Sasaki, Ryu
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Asymptotics of extreme zeros of the Meixner-Pollaczek polynomials
Journal of Computational and Applied Mathematics, 1997 The authors, in this paper study the asymptotic behaviour of the extreme zeros of the Meixner-Pollaczek polynomials (for notation see \textit{T. S. Chihara}, An introduction to orthogonal polynomials (1978; Zbl 0389.33008). A typical result is given by their Theorem (5.1) which states that the largest and smallest zeros \(X_{N,1}\) and \(X_{N,N}\) of a
Chen, Yang, Ismail, Mourad E.H.
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Wigner quantization of some one-dimensional Hamiltonians
, 2010 Recently, several papers have been dedicated to the Wigner quantization of different Hamiltonians. In these examples, many interesting mathematical and physical properties have been shown.
Berezanski Yu. M. +9 more
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Premixed flame shapes and polynomials [PDF]
, 2014 The nonlinear nonlocal Michelson-Sivashinsky equation for isolated crests of unstable flames is studied, using pole-decompositions as starting point. Polynomials encoding the numerically computed 2N flame-slope poles, and auxiliary ones, are found to ...
Denet, Bruno, Joulin, Guy
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