An experiment with electrons

Figure 18.3: Double slit experiment with electrons

We consider an experiment where an electron gun fires electrons at screen A with two slits as shown in Figure 18.3. Like bullets, electrons are discrete objects and a detector on screen B either detects the arrival of one electron or does not detect an electron. A fraction of an electron is never detected. If the firing is decreased or increased, the electron count rate at different points on screen B also decreases or increases. This count rate can be converted to a probability . If we assume that an electron arrives at a point $x$ on screen B either through slit $1$ or slit $2$ we then expect that

(18.4)

As shown in the figure this does not actually hold and at some points $P_{_{12}} <P_{_{1}} +P_{_{2}}$, just like an interference pattern. The probability is a positive quantity and it is not possible to add two probabilities and have the result go down.