#### dRic2

Gold Member

- 511

- 88

1) The Sch. Eq for a free particle is ##-\frac {\hbar}{2m} \frac {\partial ^2 \psi}{\partial x^2} = E \psi## and the solutions are plane waves of the form ##\psi(x) = Ae^{1kx} + Be^{-ikx}##. This functions can not be normalized thus they do not represent a physical phenomenon, but if I superimpose all of them with an integral on ##k## I get the "true" solution (the wave packet). This implies that a free particle with definite energy does not exist (only superposition of states with different energies can exist). This bugs me a lot. For example, think about an atom hit by an ionizing radiation: at some point an electron will be kicked out of the shell and now, if I wait some time, I have a free electron (so a free particle) and what about its energy? It should be defined by the law of conservation of energy...

2) I'm reading some lecture notes about scattering. Why does everyone take the incoming particle to be described by the state ##\psi_i = e^{i \mathbf k \cdot \mathbf r}## if it is not normalizable ? It seems to me they all assume the particle to be inside a box of length ##L## and forget about about the normalization constant. But why ?