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For questions about mathematical problems arising from quantum mechanics, a branch of physics describing the behaviour of nature at very small scales, at the level of atoms and subatomic particles.
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Existence and uniqueness for two-dimensional time-dependent Schrödinger equation
On bounded domains, for some nonlinear schrodinger equations, you might find papers by H. Brezis and T. Gallouet useful. The title of the paper is "Nonlinear Schrodinger evolution equations", and they …