Near-threshold properties of s-waves in two dimensions |
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| Harald Friedrich | |
| Technische Universität München | |
| The Schrodinger equation in two spatial dimensions is used not only to describe planar problems such as the motion of atoms adsorbed to surfaces, but also for three-dimensional systems with translational invariance in one direction, e.g., the motion of an atom or molecule near a wire or nanotube. The centrifugal potential in two dimensions contains m?-1/4 (m integer) instead of l(l+1) and is always nonvanishing, even for s waves, where it has the counterintuitive feature of being attractive.
The attractive centrifugal term substantially affects the qualitative behaviour of scattering phase shifts at small positive energies and the quantization rule at small negative energies. This talk reviews how conventional 3-D effective-range theory for above-threshold energies and a related theory for quantization just below threshold need to be modified in order to describe two-dimensional systems. |