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I was looking at simulations of a wave going through a slit. When the wavelength was much smaller than the slit width, the wave went through the slit and kept going straight like a laser beam. But when the wavelength was larger than the slit width, the wave spread in all directions when going through the slit. My question is, if a single moving neutron is ejected toward a single slit, and the neutron’s De Broglie wavelength is long compared to the slit width, then can the neutron go through the slit and take a direct right turn?

I ask this because the neutron has mass inertia, and therefore it seems odd for the neutron to take a trajectory path of going forward and then immediately turn right. Imagine you traveling a vehicle at some velocity, and then instantly turning right. The g-forces would be incredible. A wave, on the other hand, can wrap around corners. So I was thinking that the neutrons mass inertia plays a role in how sharp of an angle it can turn. I know mass inertia plays a role in the De Broglie wavelength in terms of momentum, but I'm not referring to that. I know the De Broglie wavelength changes relative to the neutron's velocity. I'm referring to the neutron’s ability or inability to take any path that a wave at the De Broglie wavelength can follow. Also I understand that the De Broglie wave is not considered to be a wave like sound such that it's made of atoms, gas, or known particles. I'm referring to a wavefunction analysis.

Another example of why I'm asking this question is the role gravity can play. For example if the slit experiment is turned sideways such that the neutron is traveling parallel to the planet. Gravity would change the trajectory path. Nothing changed in the experiment except for the addition of gravity. So it seemed to me that path probability analysis can require more than just wave analysis. I’d imagine static magnetic fields from a permanent magnet or electrically charged plates could play a role as well.

In short, I was wondering if the particle’s own inertia, gravity and other fields could significantly affect the probability path analysis. Maybe the proper way is to first do a wavefunction analysis, and then apply inertia forces, gravity, etc. Although I'm most interested in the first example of how inertia plays a role in the trajectory probability path, perhaps even preventing the particle from making too sharp of turns. If it makes any difference, I'm interested in how Many Worlds Interpretations handles this. Thanks!

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If I understand your question correctly, you are mainly concerned about the conservation of momentum. The inertia of the particle would not give any contradictions if the particle interacts with something else, which can then change the momentum of the particle. So when we consider a particle propagating (as a wave) through a slit and we end up detecting the particle at come crazy angle behind the screen, then clearly the particle must have underwent some change in momentum. Yes, indeed. If one went to a great deal of trouble, one may be able to measure to amount of momentum picked up by the screen that contains the slit and find that it matches the momentum that is missing. In other words, if the particle had to undergo a big change in momentum due to the diffraction by the slit, then the screen that contains the slit should pick up the deficit in momentum so that the sum of the momenta in the end equals the initial momentum of the particle.

Just to clear up one point, we need to remember that up until we actually detect the particle, it could be anywhere. All we know is that while it propagates through the slit is behave like a wave. The mass of the particle would affect how it propagates in that the wavefunction would a solution of a wave equation with a mass (Klein-Gordon or Dirac equation) rather than one without a mass (Helmholtz or Weyl equation).

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