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Imagine a particle in a momentum eigenstate $\vec p$ such that its wavefunction is a plane wave (or a wave packet with some width $\Delta p$ if we want this to be more realistic). Now imagine that this plane wave is elastically colliding with a thin rigid plate that is exactly perpendicular to $\vec p$. What will be the state of the plate after the collision?

If we view the particle's wave function as a superposition of localized states, each of those has some angular momentum relative to the center of the plate, and thus will cause the plate to rotate. So by the linearity of the Schrödinger equation, the plate will end up in a superposition of rotating states with different angular momenta (which will average to zero, but when measuring it we'll get some non zero value).

On the other hand, if we think of the time evolution of pure momentum states, it also seems feasible that there will only be a transfer of linear momentum, so that the plate will just move forward without rotating.

Which is correct?

Qmechanic
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J. Delaney
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1 Answers1

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It depends.

Suppose the particle is a photon and the plane is a layer of silver halide molecules like black and white photographic film. The photon would be absorbed by a particular molecule, changing it so that it would be dark when developed. Each molecule has an equal probability of being hit, but only one would be hit. That molecule would experience a recoil. If this was not at the center of mass, the film would rotate.

Suppose the particle is a photon and the plane is a silver mirror. The photon interacts with the layer of mobile electrons at the surface, making them oscillate. This absorbs the photon. The oscillating electrons radiate a new photon. Because the surface layer is extended, the reflected electron is a plane wave. It did not interact with an electron at a point. It interacted with the entire layer. The mirror would experience a rebound, but would not rotate.

See If we repeatedly divide a colorful solid in half, at what point will the color disappear?

mmesser314
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