Is the Schrödinger-Newton equation time-reversal symmetric? What about PT-symmetry or similar symmetries?
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I tried to figure it out myself. If you take the integro-differential form of the equation, a complex square of the time-dependent wavefunction appears.. It seems to me that this means the equation cannot be time symmetric but I'm not sure about this reasoning. The same goes for PT-symmetry, since the Laplacian is the same even under a P reversal
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On the N-wave Equations with PT-symmetry Vladimir S. Gerdjikov a,1 , Georgi G. Grahovski a,b,2 and Rossen I.
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