arXiv subjects

I. H. Duru

Publications and source records attributed to I. H. Duru.

22 records · Page 2Linked to original sources

arXiv1997

q-Schrodinger Equations for V=u^2+ 1/u^2 and Morse Potentials in terms of the q-canonical Transformation

The realizations of the Lie algebra corresponding to the dynamical symmetry group SO(2,1) of the Schrödinger 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 Schrödinger equation for the Morse potential is obtained from the q-deformed $V=u^2+ 1/u^2$ Schrödinger equation. Wave functions and eigenvalues of the q-Schrödinger equations yielding a new definition of the q-Laguerre polynomials are studied.

hep-th↗

arXiv1996

Scattering from the Potential Barrier V=cosh^{-2} ωx from the Path Integration over SO(1,2)

Unitary irreducible representation of the group SO(1,2) is obtained in the mixed basis, i.e. between the compact and noncompact basis and the new addition theorems are derived which are required in path integral applications involving the positively signed potential. The Green function for the potential barrier $V=cosh^{-2}ωx$ 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 $V=\cosh^{-2}ω(x-g_0t)$ are also presented.

hep-th↗

arXiv1996

A q-oscillator Green Function

By using the generating function formula for the product of two q-Hermite polynomials q-deformation of the Feynman Green function for the harmonic oscillator is obtained.

q-alg↗

arXiv1995

$sl_q(2)$ Realizations for Kepler and Oscillator Potentials and q-Canonical Transformations

The realizations of the Lie algebra corresponding to the dynamical symmetry group SO(2,1) of the Kepler and oscillator potentials are q-deformed. The q-canonical transformation connecting two realizations is given and a general definition for q-canonical transformation is deduced. q-Schrödinger equation for a Kepler like potential is obtained from the q-oscillator Schrödinger equation. Energy spectrum and the ground state wave function are calculated.

hep-th↗