Solutions to linear and nonlinear Schrödinger equations in 2D and 3D can be constructed with prescribed, arbitrarily large and highly localized spatial gradients near chosen boundary points.
Heisenberg, ¨Uber den anschaulichen Inhalt der quantentheoretischen Kinematik und Mechanik, Zeitschrift f¨ ur Physik,43(1927), 172–198
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Construction of Solutions with Extraordinary Gradient Amplification and Localization for Schr\"odinger Equations
Solutions to linear and nonlinear Schrödinger equations in 2D and 3D can be constructed with prescribed, arbitrarily large and highly localized spatial gradients near chosen boundary points.