M2L10zh_cq.txt

#
# File:   content-mit-8-421-2x-subtitles/M2L10zh_cq.txt
#
# Captions for 8.421x module
#
# This file has 30 caption lines.
#
# Do not add or delete any lines.
#
#----------------------------------------

I just want to ask you two quick questions.
I will do the perturbation theory
and I will explain everything.
But maybe you want to predict the result which
I want to derive in the next 10 minutes.
And the question is:What will we actually
get for the expectation value of H prime?
Will we get the expectation value of the dipole operator
times the electric field?
Or will we get the expectation value
of the dipole operator times the electric field over 2?
And the next question would be the same,
but what do we get for the total Hamiltonian?
So these are the questions.
I want to discuss with you in the next 10 minute simply using
perturbation theory for expectation values, 
expectation values of the total energy H naught plus H prime.
But also expectation values of the electrostatic energy
which is H prime.
The question cannot be addressed by
dimensional analysis:  what
we get is a dipole moment times an electric field.
But this is one of the situation where factors of 1/2
are not just bookkeeping.
Factors of 1/2 really reflect interesting physics.
And I want to sort of highlight it by asking you 
what would you expect would we get
for those expectation values when we solve for atomic energy
levels in an electric field?