Potential well - transition processes

This note is an update of the previous one with a new section added. Parts of
the section has been modified. The newly added section deals with only transition
processes - reflection and transmission. As explained in the class, it is somewhat
too simple to study these for the case of a finite potential well that extends to
infinity on both sides. It is instructive to do this for the case of a potential barrier
to see a worthy application with use in real physical systems - alpha decay being
a fine example. See problem #4 in the Problem set 02 (click). This note should
help you do it. As mentioned previously, the note contains what was discussed in
the class on potential well but written in a way to a more satisfactory way. Most
textbooks do not care to give clear derivations as it is a bit hazy to do it in position
space representations, namely, in terms of wavefunctions. Here we make it clearer
using bra-ket notations and provide a convincing derivation of the reflection
coefficient.


Modified note on Potential well (Click here to download)