Off the top of my head, the ONLY "infinite" potential barrier that allows a transmission is a delta function barrier. All other infinite barrier with a finite width will cause the wavefunction to be identically zero at the boundary, so no transmission!I’m think of a particle, with momentum p, that travels in a region there the potential is zero and comes to a place there it exist an infinte potential barrier and travels through the region and comes to a region there the potential is again zero. How can the particle after the barrier have the same momentum p?
You are wrong. You are forgetting that (i) this implies a reflection at the boundary and (ii) any change in momentum is due to the interaction with the potential barrier. This is no different than a classical ball-bounce-off-wall scenario!I understand that I have confused you. My thought was that I must have misunderstands something because of the explanations that stated above. The case that I did think of was an infinite potential barrier with a width, but if the wavefunction is zero at the boundary than the momentum can’t be conserved, or I’m a wrong? So if the momentum shall be conserved it most be a finite barrier, or?
Sure it is! This is because the potential field INTERACTS on the particle!If a particle, with momentum p, is travelling in a region with the potential is equal to zero, at some place the potential is not zero, if my thought above is correct than shall the potential be finite. After that the potential is again zero, is the momentum conserved?