I am trying to formulate boundary conditions and it occurred to me that I never had to implement a reflective boundary before.
The example is a one dimensional diffusion, where at $x=0$ the particles are reflected and at $x=L$ they instantly disappear in a sink.
My question now is:
Why can this be implemented by saying the flux must be zero at $x=0$ and with that due to Fick's first law the spatial derivative of the probability density? (this is what my research tells me so far)
In QM, we can confine a particle in a box by saying the wave function and with that the probability density are zero at the boundaries. Why does this not work here to create reflection?
And, secondly, I would like to get a better understanding on why the condition on the flux creates the conditions for reflection.