Abstract
We consider the Schrödinger equation for a quantum particle whose mass depends on the position of the particle on the real line. The well-posedness of the Cauchy problem is studied for the Schrödinger equation with characteristic form degenerating outside the finite segment I=[-l,l]\subset⊂ ℝ. We show that this problem generates a unitary Markovian cocycle.
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Amosov, G.G., Sakbaev, V.Z. On Self-Adjoint Extensions of Schrödinger Operators Degenerating on a Pair of Half-Lines and the Corresponding Markovian Cocycles. Mathematical Notes 76, 315–322 (2004). https://doi.org/10.1023/B:MATN.0000043458.91218.7b
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DOI: https://doi.org/10.1023/B:MATN.0000043458.91218.7b