So, this gentleman seems to think that no one has ever “derived” the Schrödinger equation before and he claims to have done so directly from Hamilton-Jacobi methods. Um, huh? He needs to read pp. 236-280 in The Conceptual Development of Quantum Mechanics by Max Jammer.
He sent me an e-mail today (in reply to one I sent to him) and still maintains his position. As I see it, there are actually two different claims that he makes. The first is that no one has ever derived the Schrödinger equation before (in any manner). I still maintain this is incorrect since I do not see how his derivation is any more a derivation than, for instance, Tom Moore’s in Unit Q of his textbook, Six Ideas That Shaped Physics. As to whether or not de Broglie’s and Schrödinger’s use of Hamilton-Jacobi methods counts in the same manner as his does, will remain an open question until I get back to my office and double-check some things (including Schrödinger’s biography and some other papers I have lying around).
Despite the fact that Schrödinger apparently admitted he “guessed” and didn’t derive his result, given Moore’s “derivation,” here is where I think the problem lies:
The Schrödinger equation essentially expresses the conservation of energy. The way Moore derives it is basically to simply attach the de Broglie relations to the standard classical wave equations. Therefore, to qualify as a true derivation it seems to me that the question revolves around whether one needs to derive the de Broglie relations as well or whether simply gluing them onto the classical wave equation can be considered a derivation of the Schrödinger equation. Either way, I’m still not entirely convinced this guy’s done what he claims he’s done. He may have found an alternative and potentially pedagogically useful way to arrive at the Schrödinger equation, but I’m not convinced it is conceptually ground-breaking.