🧵 Interpretation Probability Density Unbound States

Anonymous at Fri, 24 May 2024 21:04:46 UTC No. 16191634

What can I use the probability density of an unbound state for or how can I interpret it?
(Pic related: Plane wave hitting the potential step)

For bound states, I can integrate the probability density over a certain interval (when in 1d) and it yields the probability of measuring a particle there. This makes sense to me. Is there something similar for the unbound state?

Also, since I think this is related, why do bound states have to be normalised and unbound states not? It is often used to get rid of exponential terms in the ansatz, since they would blow up in infinity. This hower is only applied for areas, where energy is smaller than the maximum of the potential.