Eigenvalues of the two-dimensional Schrodinger equation with nonseparable potentials

The energy eigenvalues of coupled oscillators in two dimensions with quartic and sextic couplings have been calculated to a high accuracy. For this purpose, unbounded domain of the wave function has been truncated and various combination of trigonometric functions are employed as the basis sets in a Rayleigh-Ritz variational method. The method is applicable to the multiwell oscillators as well. (C) 1996 John Wiley & Sons, Inc.


Taşeli, Hasan (Wiley, 1993-01-01)
The eigenvalues of the Schrodinger equation with a polynomial potential are calculated accurately by means of the Rayleigh-Ritz variational method and a basis set of functions satisfying Dirichlet boundary conditions. The method is applied to the well potentials having one, two, and three minima. It is shown, in the entire range of coupling constants, that the basis set of trigonometric functions has the capability of yielding the energy spectra of unbounded problems without any loss of convergence providin...
Coherent states for PT-/non-PT-symmetric and non-Hermitian Morse potentials via the path integral method
KANDIRMAZ, NALAN; Sever, Ramazan (IOP Publishing, 2010-03-01)
We discuss the coherent states for PT-/non-PT-symmetric and non-Hermitian generalized Morse potentials obtained by using path integral formalism over the holomorphic coordinates. We transform the action of generalized Morse potentials into two harmonic oscillators with a new parametric time to establish the parametric time coherent states. We calculate the energy eigenvalues and the corresponding wave functions in parabolic coordinates.
Geometric measures of entanglement
UYANIK, KIVANÇ; Turgut, Sadi (American Physical Society (APS), 2010-03-01)
The geometric measure of entanglement, which expresses the minimum distance to product states, has been generalized to distances to sets that remain invariant under the stochastic reducibility relation. For each such set, an associated entanglement monotone can be defined. The explicit analytical forms of these measures are obtained for bipartite entangled states. Moreover, the three-qubit case is discussed and it is argued that the distance to the W states is a new monotone.
Exact Pseudospin Symmetric Solution of the Dirac Equation for Pseudoharmonic Potential in the Presence of Tensor Potential
AYDOĞDU, OKTAY; Sever, Ramazan (Springer Science and Business Media LLC, 2010-04-01)
Under the pseudospin symmetry, we obtain exact solution of the Dirac equation for the pseudoharmonic potential in the presence of the tensor potential with arbitrary spin-orbit coupling quantum number kappa. The energy eigenvalue equation of the Dirac particles is found and the corresponding radial wave functions are presented in terms of confluent hypergeometric functions. We investigate the tensor potential dependence of the energy of the each state in the pseudospin doublet. It is shown that degeneracy b...
Covariant Bethe-Salpeter equation for heavy Q(Q)over-bar bound states
Zakout, I; Sever, Ramazan (IOP Publishing, 1997-02-01)
We investigate a numerical solution of the covariant Bethe-Salpeter equation in the Euclidean space for heavy meson with gluon ladder in the Landau gauge and scalar confinement. A new approach is presented to solve the non-linear eigenvalue problem with suitable bases and fictitious eigenvalue parameters. We obtain unphysical states when the equation is solved for timelike spectra. We also present how to cover the singularity of a free quark propagator and Schwinger-Dyson equation when extrapolated to the ...
Citation Formats
H. Taşeli, “Eigenvalues of the two-dimensional Schrodinger equation with nonseparable potentials,” INTERNATIONAL JOURNAL OF QUANTUM CHEMISTRY, pp. 183–201, 1996, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/46675.