# Will an electron gun fire behind it?

If an electron travels as a wave, can it therefore not be aimed with any precision?

If you fire an electron gun, can't you aim it at a particular slit?

If the electron travels as a wave, will an electron gun hit anything at a 180 degree angle from the barrel? 360 degrees?

-

## 1 Answer

Electrons are not waves. Neither are they little dots of matter. The wave/particle duality means that some properties of electrons are as if they are a wave, and some are as if they are particles. They are neither, and they "travel" exactly as the hybrid quantum object they are: Unless they interact with something, they do not take on any definite trajectory.

When you "fire" an electron gun, you create an electron state that is quite sharp inside a momentum interval $[p,p + \Delta p]$, and therefore, by the Heisenberg uncertainty rather diffuse in position $[x, x +\Delta x]$. Broadly speaking, the electron will be able to reach all positions $y$ that can be reached from any of the positions inside $[x, x + \Delta x]$ with any of the momenta inside $[p,p + \Delta p]$.

Quantum mechanically, the object that tells you how likely it is to find a particle at $y$ given you know it was at $x$ a definite time $t$ before is called the propagator. The momentum you give the electron defines a set of position states the electron is initially distributed across, and calculating the propagator for each of these states (with the proper prefactor as given in the initial distribution) for a given target position $y$ will yield the probability to find the fired electron at $y$.

But the important thing is that quantum objects do not travel in the classical sense. They have (discounting Bohmian interpretations) no trajectory to speak of, they simply have probabilities to be found at $y$ after they were found at $x$.

On classical scales, the distributions of position and momenta are so sharp that the uncertainty is neglegible, and therefore, on sufficiently large scales, you could speak of "aiming" an electron gun.

-