Derivation of Schrodinger Equation from Heat Equation vs Wave

[Osher]

I pointed out recently that the Schrodinger Equation, the main nonrelativistic quantum mechanics equation, can be obtained from the heat equation and vice versa, although the same thing holds for Schrodinger equation's derivation from the Maxwell-derived wave equation. The latter is more common - for example:

1) "How to derive the Schrodinger equation," David W. Ward, Harvard U., USA, and Sabine Volkmer, MIT, USA, arXiv:physics/0610121v1 [physics.hist-ph] 17 Oct 2006.

Relationships between the Heat equation and Schrodinger equation and substitutions from one to the other are found in, for example:

2) "Symmetry and Separation of variables," Willard Miller, Jr., U. Maine USA (umn.edu), Vol. 4 of Encyclopedia of Mathematics and its Applicvations, Ed. Gian-Carlo Rota, Addison-Wesley 1977, http://ima.umn.edu/~miller/heatequation.pdf.

My 4-Interaction Probable Causation Equation Dt(u) = kDxx(u) is obtained by equating the heat and wave equations (here in 1 spatial and 1 time dimension for simplicity), as I explained here recently.

Osher Doctorow

[Osher]

It should be noted that Ward's derivation of Schrodinger equation from Maxwell's electromagnetic equations plus some elementary equations of de Broglie is very, very long and full of approximations, while simply substituting from one equation into the other and generalizing from the heat equation to imaginary variable i for the Schrodinger equation only takes a few seconds!

Schrodinger is supposed to have derived his equation similarly to Ward, but I am skeptical about that, at least regarding his initial derivation. I am beginning to think that Germany kept track of similarities between the heat and wave equations (possibly at an unpublished level, if it was regarded as a matter of "national security") and even between the Ricci and Levi-Civita tensor equations and Newton's equations, so that it had both a macroscopic and microscopic team competing, of which Einstein originally and Schrodinger were originally part (as well as Heisenberg in the microscopic team). It is remarkable that most other nations have NOT kept track of similarities between different physical equations - even the Coulomb and Newton's gravitation laws is seldom remarked upon, for example.

Osher Doctorow

[Osher]

I meant to say that the similarity between the Coulomb electrostatic law and Newton's law of universal gravitation is seldom remarked upon, at least in arXiv. It turns out to be of considerable importance for the 4-Interaction Equation above. Simiarly for the similarity between the London Equations of superconduction and Maxwell's equations of electromagnetism.

Osher Doctorow