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 Aug 16 comment Is there a physical interpretation of Neumann boundary conditions for the free Schrodinger equation on a domain? @udrv Also, yes, those more general conditions are called Robin boundary conditions. Aug 16 comment Is there a physical interpretation of Neumann boundary conditions for the free Schrodinger equation on a domain? So $n\cdot j = 0$ is equivalent to the condition that the boundary term vanishes when you integrate $\langle \Psi|\Psi^*\rangle$ by parts and that's exactly what you need to have a self-adjoint extension of the Hamiltonian. Aug 15 comment Is there a physical interpretation of Neumann boundary conditions for the free Schrodinger equation on a domain? @arivero What do you mean by "teleportation"? Identification of different sides of the domain, a la gluing a square into a torus? Aug 15 comment Is there a physical interpretation of Neumann boundary conditions for the free Schrodinger equation on a domain? @udrv So is this the idea? For a domain $D$, there are essentially two ways of fencing in a particle: either impose an infinite potential outside $D$, or impose the condition that the probability current never cross the boundary. Either way, the particle stays confined to the domain. Aug 13 comment Is there a physical interpretation of Neumann boundary conditions for the free Schrodinger equation on a domain? @arivero I'm not sure if that intuition extends to higher dimensions. For instance, in a multiply connected domain in the plane, like a thickened figure-8, collapsing the boundary to a point produces a space that's not even a manifold. In 1d, any function on an interval can be extended to a periodic function, which then descends to a function on the appropriate circle, so the analogue in higher dimensions would be functions on the appropriate torus. That's my mathematical intuition, at least; I can't really speak to the physical intuition. Aug 13 comment Is there a physical interpretation of Neumann boundary conditions for the free Schrodinger equation on a domain? Sorry about the sign issues. I added a note to the OP about this. I'm digesting your answer and will be back shortly with more questions, I'm sure. Aug 13 comment Is there a physical interpretation of Neumann boundary conditions for the free Schrodinger equation on a domain? @jac What about domains where the boundary is not totally geodesic? For instance, a disk in $\mathbb{R}^2$ where half the boundary is given Dirichlet and the other half is given Neumann? Aug 13 comment Is there a physical interpretation of Neumann boundary conditions for the free Schrodinger equation on a domain? @arivero There's not room in the post to add a third column, so I added a postscript instead :) May 11 comment Why do all the atoms of a radioactive substance not decay at the same time? I don't understand why you think me saying the derivative of an exponentially decrease is again an exponential decrease is controversial, but I have deleted the contentious section until I have time to rewrite it. May 11 comment Why do all the atoms of a radioactive substance not decay at the same time? @user121330 Ah, thank you. My probability-fu was weak: the Poisson distribution measures the probability of decay in a given length of time. May 10 comment $B$ field around an infinite wire symmetry argument As a practical example, if I make a very long current-carrying wire in a lab and run a current through it, the field I measure near the center of the wire will be the circulating magnetic field plus $b$ from the Earth's (and the Sun's, etc) magnetic field. Jul 12 comment Velocity is “Distance/Time” in a particular direction OR simply “Displacement/Time”? @AmireBendjeddou Displacement indicates direction. Jul 12 comment Velocity is “Distance/Time” in a particular direction OR simply “Displacement/Time”? They are the same thing, infinitesimally.