Modern Physics: Chapter 1 – Double Slit Experiment I

The results of the double slit experiment challenge the classical concept of the electron being a particle and the concept of nature being divided into particles and waves. Essentially you place a source of whatever you want to conduct the double slit experiment with behind a barrier that only has two narrow slits and then place a detector/screen behind that barrier and record where and when the source gets detected on the screen.

Slits Overview

Bullets

If you conduct the experiment with bullets, you should get the following result:

Slits Bullets

Where P_{1}(x), P_{2}(x) and P_{12}(x) are the probabilities of finding the particle at a given position x when the first slit is open, the second slit is open and both slits are open respectively. In the case of bullets, it is apparent that:

  • P_{12}(x) = P_{1}(x) + P_{2}(x)

But life isn’t that simple in general. If you conduct the same experiment with waves, you get a somewhat different result.

Waves

If you repeat the pattern with waves, you get the following results:

Slits Waves

when I_{1}(x), I_{2}(x) and I_{12}(x) are the intensities of the waves at a given position x when the first slit is open, the second slit is open and both slits are open respectively. Over here,

  • I_{12}(x) is clearly not simply equal to I_{1}(x) + I_{2}(x).

This is because the waves interfere with each other either constructively or destructively at different places forming interference maxima and minima at different points.

Electrons

Electrons are clearly particles right? The pattern we get by conducting the experiment with electrons will obviously be the same as the one formed by bullets, right? Wrong! When conducting the experiment with electrons, you get a result more like the one we got with waves than the one we got with bullets. Slits Electrons

Interference maxima and minima are formed. Note that unlike the experiment with waves, these are probability maxima/minima, not intensity maxima/minima.

But… electrons were particles, right? Wrong. There’s more to the story than that. To quote Shakespeare,

There are more things in heaven and earth, Horatio,
Than are dreamt of in your philosophy.

~ William Shakespeare – Hamlet

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