ON THE DERIVATION OF THE SCHRODINGER ¨ EQUATION WITH POINT-LIKE NONLINEARITY
Аннотация:
In this report we discuss the problem of approximating nonlinear delta-interactions in dimensions one and three with regular, local or non-local nonlinearities. Concerning the one dimensional case, we discuss a recent result proved in [10], on the derivation of nonlinear delta-interactions as limit of scaled, local nonlinearities. For the three dimensional case, we consider an equation with scaled, non-local nonlinearity. We conjecture that such an equation approximates the nonlinear delta-interaction, and give an heuristic argument to support our conjecture.
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