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Thanks for that, makes sense. I must be forgetting why the Schrodinger eq'n is non-dispersive, like why there isn't some first order spatial derivative, similar to the second term of this form of Black-Scholes. I think it's some assumption baked into a particular physical situation. Closed boundary conditions or something, right? It's been too long.
Holy thread necromancy, Batman! That's because it preserves total probability even under time-evolution operator (norm conservation works in both cases). Evolution over imaginary axis (ih-bar) means that the energy is redistributed, but not lost, as solution phase-space is conserved. That's the same as being 'non-dissipative.'why the Schrodinger eq'n is non-dispersive