4. We know that if we want to perform a \"double slit\" experiment with electron

Question

4. We know that if we want to perform a "double slit" experiment with electrons, the "slits" need to be spaced very close together, which is why in practice we scatter electrons off of atoms in a crystal lattice. Let's imagine that I can somehow create two actual slits that are of a similar size to the crystal atomic spacing for this problem, so that our setup is completely analogous to Young's double slit experiment for light We know that the proper mathematical description of this problem shows the electron wave function- which we approximate as an incoming plane wave diffracting through both slits. The two diffracted wave patterns then interfere with each other while heading toward the detection screen, creating a non-uniform, "lumpy" cos2-like probability density function at the screen. The physical interaction with the screen "collapses" the wave function, and the electron is observed to appear (i.e. interact with) a single position on the screen. That position is random within the constraints that statistical repetition of the process will produce results that agree with the cos2-like probability density function Someone decides that he wants to see if the electron actually passes through slit 1 or slit 2 for a given trial, so he sets up a thin screen just behind slit 1. The screen is thin enough that the electron will lose almost no kinetic energy when passing through it, but it will register a hit, or no hit on each trial When our person performs the experiment, he indeed sees that every electron seems to either pass through slit 1 (he sees a hit on his thin screen), or slit 2 (no hit detected). Most interestingly, he sees that the statistical pattern of observations on the main screen far from the two slits no longer shows the characteristic "lumpy" cos2-like interference pattern. It just looks like a bright spot directly in front of slit 1, and another bright spot directly in front of slit 2. When he takes away his thin screen behind slit 1, however, the 'lumpy" cos-like interference pattern returns. Explain why the introduction of the thin screen behind slit 1 kills the interference pattern using the concept of wave function collapse.

Explanation / Answer

Step 1 of 2

In the "double slit" experiment, the electron wave function is an incoming plane wave diffracting through both the slits.The diffracted wave patterns interfere with each other towards the detection screen forming a "nkn-uniform",Lumpy like density function at the screen. And also the physical interpretation of the screen collapses the wave function, and the electron interact with the single position on the screen.

Step 2 of 2

Since, the particles are not measured before they go throught the slits, but labelled so which the slit they o through is known. If a particle has a label when it is detected, there is no interference and the particle-like behaviour is observed.

And it appears that, it is not possible to see the interference patterns and to know which way the particles are moving simultaneously. However, observation of wave-particle duality does not require a wave function collapse.

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