0
votes
1answer
38 views

Quantum Mechanics - Rectangular Potential Barrier - Normalisation

I have a quick question regarding the normalisation of the wave function of a particle incident on a potential barrier specifically regarding the normalisation of the wave functions. The problem is ...
4
votes
2answers
194 views

Are all scattering states un-normalizable?

I am an undergraduate studying quantum physics with the book of Griffiths. in 1-D problems, it said a free particle has un-normalizable states but normalizable states can be obtained by sum up the ...
4
votes
1answer
251 views

Scattering states of Hydrogen atom in non-relativistic perturbation theory

In doing second order time-independent perturbation theory in non-relativistic quantum mechanics one has to calculate the overlap between states $$E^{(2)}_n ~=~ \sum_{m \neq n}\frac{|\langle m | H' ...
9
votes
1answer
453 views

When we define the S-matrix, what are “in” and “out” states?

I have seen the scattering matrix defined using initial ("in") and final ("out") eigenstates of the free hamiltonian, with $$\left| \vec{p}_1 \cdots \vec{p}_n \; \text{out} \right\rangle = S^{-1} ...