Géza Lévai et al 2009 J. Phys. A: Math. Theor. 42 295201 doi:10.1088/1751-8113/42/29/295201
Scattering in the 
-symmetric Coulomb potential
Géza Lévai1, Petr Siegl2,3,4 and Miloslav Znojil2
Show affiliationsScattering on the 
-symmetric Coulomb potential is studied along a U-shaped trajectory circumventing the origin in the complex x plane from below. This trajectory reflects 
symmetry, sets the appropriate boundary conditions for bound states and also allows the restoration of the correct sign of the energy eigenvalues. Scattering states are composed from the two linearly independent solutions valid for non-integer values of the 2L parameter, which would correspond to the angular momentum in the usual Hermitian setting. The transmission and reflection coefficients are written in a closed analytic form, and it is shown that, similar to other 
-symmetric scattering systems, the latter exhibit the handedness effect. Bound-state energies are recovered from the poles of the transmission coefficients.
- PACS
- MSC
-
47A75 Eigenvalue problems (See also 49R50)
- Subjects
- Dates
-
Issue 29 (24 July 2009)
Received 27 March 2009, in final form 26 May 2009
Published 30 June 2009
-
Scattering in the -symmetric Coulomb potential
Géza Lévai et al 2009 J. Phys. A: Math. Theor. 42 295201
-
Design and characterization of a planar trap
U Tanaka et al 2009 J. Phys. B: At. Mol. Opt. Phys. 42 154006
-
Linear relationship statistics in diffusion limited aggregation
Abbas Ali Saberi 2009 J. Phys.: Condens. Matter 21 465106
-
Codimension-2 surfaces and their Hilbert spaces: low-energy clues for holography from general covariance
Yakov Neiman 2009 Class. Quantum Grav. 26 245001
-
A time-dependent B-spline R-matrix approach to double ionization of atoms by XUV laser pulses
Xiaoxu Guan et al 2009 J. Phys. B: At. Mol. Opt. Phys. 42 134015
-
Molecular beam epitaxial growth and characterization of non-tapered InN nanowires on Si(111)
Yi-Lu Chang et al 2009 Nanotechnology 20 345203
-
Theory of quantum magneto-oscillations in underdoped cuprate superconductors
A S Alexandrov 2008 J. Phys.: Condens. Matter 20 192202
-
Novel multifunctional PHDCA/PEI nano-drug carriers for simultaneous magnetically targeted cancer therapy and diagnosis via magnetic resonance imaging
Sung-Baek Seo et al 2007 Nanotechnology 18 475105
-
Local and electronic structure of tribological materials: XANES analysis
A V Soldatov et al 2009 J. Phys.: Conf. Ser. 190 012072
-
KFRD Focal Plane Instruments of SODART/SRG Telescope
M Pavlinsky et al 1998 Phys. Scr. 1998 33
Users also read
What's this?- Efficient search by optimized intermittent random walks
- Soliton solutions for ABS lattice equations: I. Cauchy matrix approach
- On shell membranes of Enneper type: generalized Dupin cyclides
sigma modelRelated review articles
What's this?- Integrable structure of box–ball systems: crystal, Bethe ansatz, ultradiscretization and tropical geometry
- Lectures on localization and matrix models in supersymmetric Chern–Simons-matter theories
- Exact superconformal and Yangian symmetry of scattering amplitudes
