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One of my intro Modern Physics texts says regarding the genesis (origin) of
the Schrodinger 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?