Long ago I read on these forums that one cannot derive the Schrödinger equations because they're fundamental scientific laws. But I have noticed that I can(adsbygoogle = window.adsbygoogle || []).push({}); generatethem by making the following physical assumptions and then doing a trivial amount of substitution and differentiation:

(1) [tex] \frac {\partial ^2 \psi }{\partial x^2} + k^2 \psi = 0 [/tex]

(2) [itex] \lambda = h/p [/itex]

(3) Total energy = PE + [itex] p^2/2m [/itex]

and (4) [itex] E=h \nu [/itex]

where (4) is only needed for the time dependent form.

What bothers me is that (1) assumes a [itex] \psi [/itex] with a definite wavelength — that is — a momentum eigenfunction, and (4) was arrived at for photons, and of course the S.E.'s are used to deal with wavefunctions that are not necessarily momentum eigenfunctions and for particles that are not photons.

Thoughts?

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# I About the premises behind the Schrödinger equations

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