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Dec 9, 2017 at 11:59 comment added Jan Bos @J.G. I meant my reply to his comment to my question. So you can find it above.
Dec 9, 2017 at 8:26 comment added J.G. @JanBox Could you link to the Zheng Liu example?
Dec 9, 2017 at 2:27 comment added Jan Bos Your answer does not prove that such an equation does not exist. It just gives an example of one that does not work. Per my comment under my question in response to Zheng Liu I also am not convinced on your statement that there is more information in $\psi$ than in $\rho$. You probably could say at most that the state at point $x = x_1$ contains more information than $\rho$ at the single point $x = x_1$.
Dec 7, 2017 at 20:35 comment added Mauricio Sorry for the confusion in many Europeans schools they use the probability current to calculate transmission/reflection coefficients, nevertheless these problems still need Schrodinger equation: cp3.irmp.ucl.ac.be/~maltoni/PHY1222/QM-IVa.pdf
Dec 7, 2017 at 12:44 comment added J.G. @Mauricio If you come up with an example, you should probably mention it in an answer here, even if it's only "a long comment".
Dec 7, 2017 at 10:06 comment added Mauricio Yeah, but if I remember correctly you can solve certain scattering introductory problems using continuity equation only and without using $\psi$.
Dec 7, 2017 at 10:01 comment added J.G. Mauricio Yes, but $\mathbf{j}$ is $\psi$-dependent
Dec 7, 2017 at 9:59 comment added Mauricio You can write an equation for $\rho$ and $J$ (the probability current) though.
Dec 7, 2017 at 7:33 history answered J.G. CC BY-SA 3.0