![]() Imagine decomposing $f$ into a single plane wave modulated by an envelope function $\psi(x)$: $f(x) = \psi(x)\, e^ c_n' (iz)^n$. Where deriving the equation, achrdinges assumed that nucleus is surrounded a vibrating electen ware which are produced by. Take a general solution $f(x)$ to the wave equation $\partial^2 f = 0$ (we use Lorentz-covariant notation and the -+++ sign convention). As Joe points out in his answer to a duplicate, the Schrodinger equation for a free particle is a variant on the slowly-varying envelope approximation of the wave equation, but I think his answer misses some subtleties. ![]()
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