Today a student asked a question that I had not considered
before. I think I know the answer but am not 100% sure. Please
let me know if I am on the right track.
The question... If Schrodinger's equations only tell us the
probability of an electron being in any particular energy state
and therefore a non zero probability exists that it will be in
various unusual states, why do we not see the entire visible
spectrum when we look at the emission spectrum of excited atoms?
I thought for awhile and said I would give my best guess but
warned it was only my best guess. I told her that in effect we
could see the entire spectrum because any particular electron
could possibly be changed from any energy level to any other
level. However the probability for the energy changes
represented by the dark space between spectral lines is extremely
low. Therefore any light generated with such energy would be
very infrequent and not detectable with normal means. How did I
do?