Hardy uncertainty principle for the linear Schrödinger equation on regular quantum trees. (English) Zbl 1491.35375
Summary: In this paper we consider the linear Schrödinger equation (LSE) on a regular tree with the last generation of edges of infinite length and analyze some unique continuation properties. The first part of the paper deals with the LSE on the real line with a piece-wise constant coefficient and uses this result in the context of regular trees. The second part treats the case of a LSE with a real potential in the framework of a star-shaped graph.
MSC:
| 35Q41 | Time-dependent Schrödinger equations and Dirac equations |
| 35R02 | PDEs on graphs and networks (ramified or polygonal spaces) |
| 35B60 | Continuation and prolongation of solutions to PDEs |
| 81Q35 | Quantum mechanics on special spaces: manifolds, fractals, graphs, lattices |
| 35A02 | Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness |
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