# Particle in a Box Question .

1. Sep 30, 2014

### terp.asessed

I've been wondering, if an electron in a box (of length L) is NOT a wave, what is the probability density in this non-quantum mechanical case?

2. Sep 30, 2014

### Staff: Mentor

Non Quantum Mechanical case - don't get it.

But its not a wave in any usual physical sense. To see it the wave propagates in an abstract infinite dimensional Hilbert space.

The wave particle duality is a crock of the proverbial that was outdated when Dirac came up with his transformation theory in about 1927.

It persists today purely because of the semi-historical approach most textbooks take.

To see the real basis of QM check out:
http://www.scottaaronson.com/democritus/lec9.html

For a correct treatment of QM have a look at the first 3 chapters of Ballentine - it may be a revelation - it was for me:
https://www.amazon.com/Quantum-Mechanics-A-Modern-Development/dp/9810241054

Thanks
Bill

Last edited by a moderator: May 7, 2017
3. Sep 30, 2014

### Staff: Mentor

The electron is never a wave, no more so in quantum mechanics than in classical mechanics. Bhobba's observation about a "crock of the proverbial..." is indelicate but accurate.

But you're asking about the probability density for the position of the electron when quantum effects are insignificant. That will be $\rho(x)=\delta(x-X)$ where $X$ is the classical position and $\delta$ is the Dirac delta function. This solution is not physically realizable, although it is easy to construct situations (for example, all of classical mechanics) where it's a useful idealization.

Last edited: Sep 30, 2014
4. Sep 30, 2014

### terp.asessed

Thank you!!!!!!! I think I get it.