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Re: Schrodinger equation origins

The first result in my G * . search is:

<... According to Schroedinger's ideas [bc emphasis], classical
dynamics of point particles should correspond to the " geometrical
optics " limit of a linear wave equation, in the same way as ray optics
is the limit of wave optics. It is shown that, using notions of modern
wave theory, the " geometrical optics " analogy leads to the
correspondence between a classical Hamiltonian H and a " quantum " wave
equation in a natural and general way. In particular, the correspondence
is unambiguous also in the case where H contains mixed terms involving
momentum and position. In the line of Schroedinger's ideas, it is also
attempted to justify the occurrence, in QM, of eigenvalues problems, not
merely for energy, but also for momentum. It is shown that the wave
functions of pure momentum states can be defined in a physically more
satisfying way than by assuming plane waves. In the case of a spatially
uniform force field, such momentum states have a singularity and move
unreformed according to Newton's second law. ...>

I think this book (follows result # 6>) is likely among the better
expositions of his development.



p.s. For heuristic purpose, Eisberg devotes ~ 6 pp. (section 5.2 of
"Quantum Physics of Atoms, etc.) to: "Now the first problem at hand is
not how to solve a certain differential equation; instead, the problem
is how to "find" the equation."

Larry Smith wrote:

One of my intro Modern Physics texts says regarding the genesis (origin) of
the Schro[e]dinger wave equation "Like the classical wave equation, the
Schrodinger equation relates the time and space derivatives of the wave
function. Schrodinger's reasoning is somewhat difficult to follow and is
not important for our purposes. In any case, the Schrodinger equation
cannot be derived, just as Newton's laws of motion cannot be derived."

Can the list give me a sense of Schrodinger's line of reasoning in
developing his wave equation?