What Is the Probability Density of a Non-Wave Electron in a Box?

[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?

 

[bhobba]

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The wave particle duality is a crock of the proverbial that was outdated when Dirac came up with his transformation theory in about 1927.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/dp/9810241054/?tag=pfamazon01-20

Thanks
Bill

 

[Nugatory]

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?

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.

 

[terp.asessed]

Thank you! I think I get it.