# Linear combination of two solutions of the simplified schroedinger equation

1. Jun 4, 2012

### freddyfish

This is, when it all comes around, just math. I am asked to prove that if the schroedinger equation looks like:

$\frac{d^{2}}{dx^{2}}$ψ=-$\frac{4πm}{h}$*[E-U(x)]ψ(x)

and ψ1 and ψ2 are two separate solutions for the same potential energy U(x), then Aψ1 + Bψ2 is also a solution of the equation.

I am asking this because I think it is obvious that the last solution also satisfies the S.E. if the two terms of it are two individual solutions.

To show that the linear combination is also a solution all you have to do is replace ψ by Aψ1 + Bψ2 in the differential equation, but this feels more like confirming rather than proving. Since I'm pretty new to this quantum mechanic discipline, I would prefer a simple proof, and if there is no simple proof that is more of a proof than a confirmation of the statement, then I have probably already answered the question in the way intended.

Thanks //F

2. Jun 4, 2012