One-dimensional Dirac operators with zero-range interactions: Spectral, scattering, and topological results
Abstract
The spectral and scattering theory for 1-dimensional Dirac operators with mass m and with zero-range interactions are fully investigated. Explicit expressions for the wave operators and for the scattering operator are provided. These new formulae take place in a representation which links, in a suitable way, the energies -∞ and +∞, and which emphasizes the role of m. Finally, a topological version of Levinson's theorem is deduced, with the threshold effects at m automatically taken into account.
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