Deriving Schrodinger's Equation w/o Boundary Conditions

[pieterenator]

This paper illustrate a simple derivation of the Schroedinger equation
Would you be very suspicious of logical and/or mathematical errors in it?

http://arxiv.org/abs/physics/0610121

Haha... "simple" is relative.

Also, this is not a "derivation" the way I meant it. That is to say, they're not using fundamental rules to prove new rules, they're "generalizing" and "approximating." It's safe to say that they probably wouldn't know how to generalize and approximate if they didn't know what the end result "should" be (the Schroedinger Equation). Back before quantum mechanics, if somebody used this kind of argument to justify a new "master equation," he would have been laughed at. The reason the Schroedinger equation was accepted was because of the empirical evidence for it, not because someone somehow derived it.

Not that this kind of thing doesn't have any value. And I'm not implying that they made any unacceptable logical leaps. I'm just saying that they didn't strictly prove Schroedinger's Equation using classical (or relativistic) principles... they had to extend, generalize, and approximate.

But the answer is yes. I would be very suspicious. Justifiably so.

 

[reilly]

Absolutely correct; pieterenator has it exactly right. In the cited paper, there's nothing more than a plausibility argument, and a nice one at that.

There is no derivation of the Schrodinger E., nor of the 2nd Law of Newton, nor of the Conservation of anything,...Indeed, to the uncritical, non-Humean eye, Noether's Thrm is a derivation of Conservation Laws -- but how could we even begin to examine all the assumptions that lurk behind Emily Noether, which must be done in order to give a sound evaluation of derivation vs. plausibility argument?

Who cares, if nothing can be derived? All we can do is make our best guess, and see what happens. This is as true for Newton as it is for Einstein, Heisenberg, et. all. Elegant as their work is, no one believed any of it until the work was successfully checked by experiment. Mathematicians use axioms; physicists use experiments.

Regards,
Reilly Atkinson

 

[samalkhaiat]

There is no derivation of the Schrodinger E., nor of the 2nd Law of Newton

If the chosen set of axioms does not contain Schrodinger/ Newton equations, then the formalisim should provide ways for DERIVING them from the axioms. Any failure means that your axioms contain a piece of garbage.

...Indeed, to the uncritical, non-Humean eye, Noether's Thrm is a derivation of Conservation Laws -- but how could we even begin to examine all the assumptions that lurk behind Emily Noether, which must be done in order to give a sound evaluation of derivation vs. plausibility argument?

Noether's theorem is a THEOREM! "given A, then B"; where A is the invariance under some Lie group, and B is a statement about a conserved quantity that can be DERIVED SYSTEMATICALLY from the action integral. If this is not a derivation, can you tell us what is it that we do when we play with equations and produce B from A?

Who cares, if nothing can be derived?

I do, because I lose my job if I cann't derive anything!

Mathematicians use axioms; physicists use experiments.

I am a physicist and I only care about a self-consistent set of axioms, I leave experiments for the more able peopel who work on them!

Regards

sam