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In this paper we consider the linear Schrodinger equation (LSE) on a regulartree with the last generation of edges of infinite length and analyze someunique continuation properties. The first part of the paper deals with the LSEon the real line with a piece-wise constant coefficient and uses this result inthe context of regular trees. The second part treats the case of a LSE with areal potential in the framework of a star-shaped graph.

Hardy uniqueness principle for the linear Schrodinger equation on quantum regular trees