Question

I'm trying to understand the Schrodinger wave equation. We talked about it in my calculus based general physics 2 course last semester and used it to find orbitals, but I want to understand how it's derived. What do I need to know, should I learn linear algebra first?

If anyone can point me in the right direction, that'd be great!

Answer 1

My understanding is that the wave equation as Schrodinger put it is not derived, but taken as a postulate, like F=ma. Newton did not derive that he assumed it and used it to form the rest of mechanics. In my QM class we were shown reasons why he thought it might be a certain way and not another way, but in the end we were told he just created the wave equation and used it to see if it got the observed results. Someone on this forum may know something different, but my text says basically this.

Answer 2

The wave equation is a part of the Shrodinger equation, in addition to the potential, V(x). Solutions for the Shrodinger equation can require solving differential equations. That might be more helpful to study, rather than linear algebra.

Answer 3

To understand the devolopemnt of the Schrödinger equation, u should get familiar with what is called the old quantom theory.
and that is the basic wave particle duality that arose from the photoelectric effect, and
The de Broglie relations.

http://en.wikipedia.org/wiki/De_Broglie_hypothesis

To each particle there is wave function related.
Or otherwise to each light wave u can relate a particle (photon)
where the enrgy of the particle is

(1) E=w*h/2pi (or h bar)
and it's momentom
P=k*h/2pi

now take the regular wave equation
\[\Psi=\exp(i(kx-wt))\]

and partial derivatives, one by time and one by x

replace w with (1) w=E/h (bar)
and k the same way.


and now u should be familiar with operators and eigenvalus (not very hard to learn with wikipedia)
and it;s almost done...
I can go thorugh with u over it but now a little tired to finish it here...

check this (in Hebrew but the equations are good)
http://he.wikipedia.org/wiki/%D7%9E%D7%A9%D7%95%D7%95%D7%90%D7%AA_%D7%A9%D7%A8%D7%93%D7%99%D7%A0%D7%92%D7%A8


tnx for the quastion!
good night :)