Quantum motion on a half-line connected to a plane

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Abstract
In this paper, the free motion of a particle on a manifold that consists of a one-dimensional and a two-dimensional part connected in one point is discussed. The class of admissible Hamiltonians is found using the theory of self-adjoint extensions. Particular attention is paid to those Hamiltonians that allow the particle to pass through the point singularity; the reflection coefficient and other quantities characterizing scattering on the connection point are calculated. A possible application is also discussed.

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