On the Non-Linear Schrödinger Equation
When a homogeneous electron beam passes through a small hole, a well-known diffraction picture is obtained according to quantum mechanics. This picture does not depend on the density of the electrons, since the Schrödinger equation is linear. Experiment contradicts however this deduction, because in reality the beam dilates. Accordingly, a generalized nonlinear Schrödinger equation is here proposed which gives both a diffraction picture and the dilatation phenomenon. Attempts to check these effects may turn into a crucial experiment.
KeywordsSchrodinger Equation Hartree Equation Crucial Experiment Diffraction Picture Coulomb Potential Energy
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