16 research outputs found
Scattering of Dirac particles from non-local separable potentials: the eigenchannel approach
An application of the new formulation of the eigenchannel method [R.
Szmytkowski, Ann. Phys. (N.Y.) {\bf 311}, 503 (2004)] to quantum scattering of
Dirac particles from non-local separable potentials is presented. Eigenchannel
vectors, related directly to eigenchannels, are defined as eigenvectors of a
certain weighted eigenvalue problem. Moreover, negative cotangents of
eigenphase-shifts are introduced as eigenvalues of that spectral problem.
Eigenchannel spinor as well as bispinor harmonics are expressed throughout the
eigenchannel vectors. Finally, the expressions for the bispinor as well as
matrix scattering amplitudes and total cross section are derived in terms of
eigenchannels and eigenphase-shifts. An illustrative example is also provided.Comment: Revtex, 9 pages, 4 figures, published versio
Mathematical Properties of a New Levin-Type Sequence Transformation Introduced by \v{C}\'{\i}\v{z}ek, Zamastil, and Sk\'{a}la. I. Algebraic Theory
\v{C}\'{\i}\v{z}ek, Zamastil, and Sk\'{a}la [J. Math. Phys. \textbf{44}, 962
- 968 (2003)] introduced in connection with the summation of the divergent
perturbation expansion of the hydrogen atom in an external magnetic field a new
sequence transformation which uses as input data not only the elements of a
sequence of partial sums, but also explicit estimates
for the truncation errors. The explicit
incorporation of the information contained in the truncation error estimates
makes this and related transformations potentially much more powerful than for
instance Pad\'{e} approximants. Special cases of the new transformation are
sequence transformations introduced by Levin [Int. J. Comput. Math. B
\textbf{3}, 371 - 388 (1973)] and Weniger [Comput. Phys. Rep. \textbf{10}, 189
- 371 (1989), Sections 7 -9; Numer. Algor. \textbf{3}, 477 - 486 (1992)] and
also a variant of Richardson extrapolation [Phil. Trans. Roy. Soc. London A
\textbf{226}, 299 - 349 (1927)]. The algebraic theory of these transformations
- explicit expressions, recurrence formulas, explicit expressions in the case
of special remainder estimates, and asymptotic order estimates satisfied by
rational approximants to power series - is formulated in terms of hitherto
unknown mathematical properties of the new transformation introduced by
\v{C}\'{\i}\v{z}ek, Zamastil, and Sk\'{a}la. This leads to a considerable
formal simplification and unification.Comment: 41 + ii pages, LaTeX2e, 0 figures. Submitted to Journal of
Mathematical Physic
Discrete symmetries, spectra, degeneracies, cross sections: a toy model with interactions centred at the vertices of Platonic solids
International audienc
Critical points for finite Fibonacci chains of point delta-interactions and orthogonal polynomials
International audienc
Normalization of states for a quantum magnetic circular billiard
International audienc
Two-dimensional Helmholtz equation with zero Dirichlet boundary condition on a circle: Analytic results for boundary deformation, the transition disk-lens
International audienc
Quantum circular billiards : further analytical results
International audienc
Bound states for two dimensional Schrödinger equation with anisotropic interactions localized on a circle
International audienc
Two-dimensional quantum scattering by non-isotropic interactions localized on a circle, applications to open billiards
International audienc