This is, when it all comes around, just math. I am asked to prove that if the schroedinger equation looks like:(adsbygoogle = window.adsbygoogle || []).push({});

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

and ψ_{1}and ψ_{2}are two separate solutions for the same potential energy U(x), then Aψ_{1}+ Bψ_{2}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 Aψ_{1}+ Bψ_{2}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

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# Linear combination of two solutions of the simplified schroedinger equation

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