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Öğe Green function on the q-symmetric space SUq(2)/U(1)(Iop Publishing Ltd, 1998) Ahmedov, H; Duru, IHInvariant distance on the non-commutative C*-algebra C(SUq(2)) is constructed and the generalized functions on the q-symmetric space M = SUq(2)/U(1) are introduced. The Green function and the kernel on M are derived. A path integration is formulated. The Green function for the free massive scalar field on the non-commutative Einstein space R-1 x M is presented.Öğe Green function on the quantum plane(Iop Publishing Ltd, 1999) Ahmedov, H; Duru, IHA Green function (which can be called q-analogous of the Hankel function) on the quantum plane E-q(2) = E-q(2)/U(1) is constructed.Öğe On the invariant distance and Green function for SUq(2)(Inst Physics Acad Sci Czech Republic, 1997) Ahmedov, H; Duru, IHFollowing the introduction of the invariant distance on the non-commutative C-algebra of the quantum group SUq(2) the Green function on the q-Podler's sphere M-q = SUq(2)/U(1) is derived. Possible applications are briefly discussed.Öğe A q-oscillator Green's function(Amer Inst Physics, 1997) Ahmedov, H; Duru, IHBy using the generating function formula for the product of two q-Hermite polynomials, q-deformation of the Feynman Green's function for the harmonic oscillator is obtained. (C) 1997 American Institute of Physics.Öğe q-Schrodinger equations for V=u(2)+1/u(2) and Morse potentials in terms of the q-canonical transformation(World Scientific Publ Co Pte Ltd, 1997) Dayi, OF; Duru, IHThe realizations of the Lie algebra corresponding to the dynamical symmetry group SO(2, 1) of the Schrodinger equations for the Morse and the V = u(2) + 1/u(2) potentials were known to be related by a canonical transformation. q-deformed analog of this transformation connecting two different realizations of the sl(q)(2) algebra is presented. By the virtue of the q-canonical transformation, a q-deformed Schrodinger equation for the Morse potential is obtained from the q-deformed V = u(2)+1/u(2) Schrodinger equation. Wave functions and eigenvalues of the q-Schrodinger equations yielding a new definition of the q-Laguerre polynomials are studied.Öğe Quantum mechanical motions over the group manifolds and related potentials(Plenum Press Div Plenum Publishing Corp, 1995) Duru, IH[Abstract Not Available]Öğe Quantum mechanical problems with q-deformations and over the p-adic number fields(Plenum Press Div Plenum Publishing Corp, 1997) Duru, IH[Abstract Not Available]Öğe Representations of SU(1,1) in non-commutative space generated by the Heisenberg algebra(Iop Publishing Ltd, 2001) Ahmedov, H; Duru, IHSU(1, 1) is considered as the automorphism group of the Heisenberg algebra H. The basis in the Hilbert space K of functions on H on which the irreducible representations of the group are realized is explicitly constructed. From group theoretical considerations summation formulae for the product of two, three and four hypergeometric functions are derived.Öğe Scattering from the potential barrier V=cosh(-2)wx from the path integration over SO(1,2)(Iop Publishing Ltd, 1997) Ahmedov, H; Duru, IHUnitary irreducible representation of the group SO(1,2) is obtained in the mixed basis, i.e, between the compact and non-compact bases, and new addition theorems are derived which are required in path integral applications involving a positively signed potential. The Green function for the potential barrier V = cosh(-2) omega is evaluated from the path integration over the coset space SO(1,2)/K where K is the compact subgroup. The transition and the reflection coefficients are given. Results for the moving barrier V = cosh(-2) omega(x - g(0)t) are also presented.Öğe Summation formulae for the product of the q-Kummer functions from Eq(2)(Iop Publishing Ltd, 2001) Ahmedov, H; Duru, IHUsing the representation of E-q(2) on the non-commutative space zz* - qz*z = a; q < 1, > 0 summation formulae for the product of two, three and four q-Kummer functions are derived.Öğe Unitary representations of the two-dimensional Euclidean group in the Heisenberg algebra(Iop Publishing Ltd, 2000) Ahmedov, H; Duru, IHE(2) is studied as the automorphism group of the Heisenberg algebra H. The basis in the Hilbert space K of functions on H on which the unitary irreducible representations of the group are realized is explicitly constructed. The addition theorem for the Kummer functions is derived.Öğe Vacuum structures for the charged fields in presence of E-M potentials and boundaries(Plenum Press Div Plenum Publishing Corp, 1997) Duru, IH[Abstract Not Available]
