Conformal mapping and bound states in bent waveguides

Journal Article · Thu Dec 23 00:00:00 EST 2010 · AIP Conference Proceedings

DOI:https://doi.org/10.1063/1.3537857· OSTI ID:21511342

Sadurni, E; Schleich, W P ^[1]

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1. Institut fuer Quantenphysik, Ulm Universitaet, Albert-Einstein Allee 11 89081 Ulm (Germany)

Is it possible to trap a quantum particle in an open geometry? In this work we deal with the boundary value problem of the stationary Schroedinger (or Helmholtz) equation within a waveguide with straight segments and a rectangular bending. The problem can be reduced to a one-dimensional matrix Schroedinger equation using two descriptions: oblique modes and conformal coordinates. We use a corner-corrected WKB formalism to find the energies of the one-dimensional problem. It is shown that the presence of bound states is an effect due to the boundary alone, with no classical counterpart for this geometry. The conformal description proves to be simpler, as the coupling of transversal modes is not essential in this case.

• OSTI ID: 21511342
• Journal Information: AIP Conference Proceedings, Vol. 1323, Issue 1; Conference: Symposium on symmetries in nature in memoriam Marcos Moshinsky, Cuernavaca (Mexico), 7-14 Aug 2010; Other Information: DOI: 10.1063/1.3537857; (c) 2010 American Institute of Physics; ISSN 0094-243X
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
BOUNDARY-VALUE PROBLEMS
CONFORMAL MAPPING
COUPLING
FUNCTIONAL ANALYSIS
ONE-DIMENSIONAL CALCULATIONS
SCHROEDINGER EQUATION
TRAPS
WAVEGUIDES
WKB APPROXIMATION
APPROXIMATIONS
CALCULATION METHODS
DIFFERENTIAL EQUATIONS
EQUATIONS
MAPPING
MATHEMATICS
PARTIAL DIFFERENTIAL EQUATIONS
TOPOLOGICAL MAPPING
TRANSFORMATIONS
WAVE EQUATIONS