منابع مشابه
Quasi Exactly Solvable Difference Equations
Several explicit examples of quasi exactly solvable ‘discrete’ quantum mechanical Hamiltonians are derived by deforming the well-known exactly solvable Hamiltonians of one degree of freedom. These are difference analogues of the well-known quasi exactly solvable systems, the harmonic oscillator (with/without the centrifugal potential) deformed by a sextic potential and the 1/ sin x potential de...
متن کاملOn Some Solvable Difference Equations and Systems of Difference Equations
AND APPLIED ANALYSIS, Vol. 2012, No. Article ID 54176, pp. 1-11, Nov, 2012 References: Abstract: Here, we give explicit formulae for solutions of some systems of difference equations, which extend some very particular recent results in the literature and give natural explanations for them, which were omitted in the previous literature.
متن کاملMulti-Particle Quasi Exactly Solvable Difference Equations
Several explicit examples of multi-particle quasi exactly solvable ‘discrete’ quantum mechanical Hamiltonians are derived by deforming the well-known exactly solvable multi-particle Hamiltonians, the Ruijsenaars-Schneider-van Diejen systems. These are difference analogues of the quasi exactly solvable multi-particle systems, the quantum Inozemtsev systems obtained by deforming the well-known ex...
متن کاملSome Functional-difference Equations Solvable in Finitary Functions
The following equation is considered: q(−i∂/∂x)u(x) = (f ∗ u)(Ax), where q is a polynomial with complex coefficients, f is a compactly supported distribution, and A : Rn → Rn is a linear operator whose complexification has no spectrum in the closed unit disk. It turns out that this equation has a (smooth) solution u(x) with compact support. In the one-dimensional case, this problem was treated ...
متن کاملBethe ansatz solutions to quasi exactly solvable difference equations
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. These equations are deformation of the well-known exactly solvable difference equations of the Meixner–Pollaczek, continuous Hahn, continuous dual Hahn, Wilson and Askey–Wilson polynomials. Up to ...
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ژورنال
عنوان ژورنال: Journal of Mathematical Physics
سال: 2007
ISSN: 0022-2488,1089-7658
DOI: 10.1063/1.2818560