Exploring the deBroglie Function: Understanding Its Mathematical Signature

[jostpuur]

meopemuk, have you been able to derive this relativistic Shrodinger's equation out of relativistic Lagrangian $L=-mc^2\sqrt{1-|v|^2/c^2}$ with Feynman's path integral (or so called slice of path integral)? I've noticed it is notably more difficult than in non-relativistic case. At least I haven't been able to do it.

I was quite suprised when I noticed last night, that the Klein-Gordon equation actually does conserve probability, if only positive frequency solutions are considered. Are you aware of this?

btw this discussion has got quite far from the original post, but I guess it doesn't disturb anyone... :tongue2:

 

[meopemuk]

meopemuk, have you been able to derive this relativistic Shrodinger's equation out of relativistic Lagrangian $L=-mc^2\sqrt{1-|v|^2/c^2}$ with Feynman's path integral (or so called slice of path integral)? I've noticed it is notably more difficult than in non-relativistic case. At least I haven't been able to do it.

No I haven't tried to do that. Personally I find least action, Lagrangian, and path integral methods more confusing than illuminating. Perhaps, it's just me.

I was quite suprised when I noticed last night, that the Klein-Gordon equation actually does conserve probability, if only positive frequency solutions are considered. Are you aware of this?

Even if this is so, it wouldn't convince me that the Klein-Gordon equation can be treated as an analog of the Schroedinger equation for relativistic particles. I've just written a long post about this in https://www.physicsforums.com/showpost.php?p=1379494&postcount=171

btw this discussion has got quite far from the original post, but I guess it doesn't disturb anyone... :tongue2:

It doesn't disturb be. We can open a new thread if somebody is disturbed.

Eugene.