How are probabilistic equations of physics usually formulated?

[Mingy Jongo]

Are they derived from accepted laws and then tested, or are experiments carried out first and then a function is searched for that matches the results (or possibly both, or neither)? For example, how would an equation that gives the probability of electron locations be thought of? My "gut feeling" is that the former would be done, as the equations I've seen seem too precise to be otherwise, but as I do not have much experience in this field, I thought it would be better to ask.

 

[Runner 1]

Are they derived from accepted laws and then tested, or are experiments carried out first and then a function is searched for that matches the results (or possibly both, or neither)? For example, how would an equation that gives the probability of electron locations be thought of? My "gut feeling" is that the former would be done, as the equations I've seen seem too precise to be otherwise, but as I do not have much experience in this field, I thought it would be better to ask.

I asked my QM professor this. He said Schrödinger just randomly decided to take the (well known) wave equation for string vibrations, etc. and modify it until it fit experimental data. Seems kind of sketchy to me... but hey, he has a Ph.D. :P

 

[jtbell]

No, Schrödinger did not proceed randomly, but was inspired by an analogy: quantum mechanics is to classical mechanics as wave optics is to geometrical (ray) optics. For some more details, see here:

https://www.physicsforums.com/showthread.php?p=418069#post418069

 

[Runner 1]

No, Schrödinger did not proceed randomly, but was inspired by an analogy: quantum mechanics is to classical mechanics as wave optics is to geometrical (ray) optics. For some more details, see here:

https://www.physicsforums.com/showthread.php?p=418069#post418069

Nice post that you've linked to. I've always wondered why people feel compelled to make up answers instead of just saying "I don't know".