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What is the second-lowest value of the energy E?
Show that this value of the energy is shared by three
distinct states. Here we say that the degeneracy is g=3.
Write the wave functions for each of the states and show
that one is cylindrically symmetric about the x-axis, while another
is cylindrically symmetric about the y-axis and the third is
cylindrically symmetric about the z-axis. States of this type
should be familiar from chemistry class. The three states you are
looking at are 
, 
and 
states respectively.
Specify an experiment by which these
states may be distinguished. Justify that your experiment
gives different results for the three states. The fact that these
states are distinct but related to one another by simple symmetry
operations (rotations) which do not affect 
is closely
related to the fact that this energy level is degenerate.
Prof. Tomas Alberto Arias
Thu Oct 12 17:23:22 EDT 1995