Schrodinger-Poisson system: Difference between revisions

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The Schrodinger-Poisson system

iv_{t}^{+}+\Delta v/2=uv^{+}\,

iv_{t}^{-}-\Delta v/2=uv^{-}\,

\Delta u=-|v^{+}|^{2}+|v^{-}|^{2}\,

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 The '''Schrodinger-Poisson system'''
-<center><math>i v^+_t + \Delta v/2 = u v^+ </math></center>
+<center><math>i v^+_t + \Delta v/2 = u v^+ \,</math></center>
-<center><math>i v^-_t - \Delta v/2 = u v^- </math></center>
+<center><math>i v^-_t - \Delta v/2 = u v^- \,</math></center>
-<center><math>\Delta u = - |v^+|^2 + |v^-|^2</math></center>
+<center><math>\Delta u = - |v^+|^2 + |v^-|^2\,</math></center>
 arises as the [[non-relativistic limit]] of the [[NLW|nonlinear Klein-Gordon equation]].