Superposition principle and continuity

[sciboudy]

hello
i have question : how the superposition principle proves continuity of ψ in potential barrier

 

[sciboudy]

and how to prove the continuity of psi

 

[mfb]

Does this question have any context? Book/paper/whatever?
A discontinuous wave function cannot satisfy the Schroedinger equation (it does not have a spatial derivative), but this has no clear relation to superposition. And it is independent of any explicit potentials.

 

[sciboudy]

okay ... but how to prove continuity of psi by super position ? example in potential barrier

 

[Fredrik]

okay ... but how to prove continuity of psi by super position ? example in potential barrier

I don't understand the "by superposition" requirement. Since ψ satisfies the Schrödinger equation, it's differentiable, and every differentiable function is continuous.

 

[Naty1]

Been too long for me to remember details, but I think you can get your answer here:

http://en.wikipedia.org/wiki/Superposition_principle#Quantum_superposition

especially quantum superposition...

Schrödinger equation IS linear, and the superposition principle holds because, by definition, a linear system must be additive...is THAT what you mean??