Probability Density of Electron in EM & Matter Waves

[nklohit]

I realized that, in EM wave, the intensity is proportional to the sqare of the fileds, and the fileds obey the wave eqation, then the intensity is proportional to the sqaure of the wave eqaution. And in electron matter wave, the probability density to find electron is proportional to the absolute square of wave equation, too. But what is the reason that the probability density to find electron is equal to the absolute square of wave equation?

 

[jtbell]

The wave function in QM is complex. The ordinary square of a complex number is another complex number, in general. But probabilities are real numbers. In order to get real probabilities out of a complex wave function, we need to use the absolute square (or something similar).

 

[lalbatros]

Not al probabilties are like that.
In statistical mechanics the probabilities can add up.
In QM the amplitude add up, and this only can lead to interference and wave-like phenomena.

 

[cgw]

I had trouble with this also. I thought I was missing something simple until I realized (and correct me if I am wrong) that Born received the Nobel prize for figuring it out.

 

[CarlB]

As far as QM goes (as opposed to QFT), it is possible to rewrite the theory to get an equivalent theory that works with probabilities instead of amplitudes. It's called Bohmian mechanics.

For understanding why amplitudes need to be discussed instead of probabilities, one can suppose that the quantum state truly does exist, but not as a probability density. For example, it could be some sort of wave equation method of calculating a stress in space-time. Then the probability postulate just means that the actual result is random, but is proportional to how much stress that is aligned with that result.