M1L1d.txt

#
# File:   content-mit-8-421-1x-subtitles/M1L1d.txt
#
# Captions for 8.421x module
#
# This file has 47 caption lines.
#
# Do not add or delete any lines.
#
#----------------------------------------

OK, let's work that out a little bit.
I'll give you some examples.
So the phenomenon of a two-level system is it has saturation.
The maximum energy you can put in is one quantum.
Whereas an harmonic oscillator can never be saturated.
Just to think of the harmonic oscillator potential parabola,
you can drive the system as high as you want.
So you can go in this classic language
to arbitrarily large amplitudes.

So what I just mentioned where the equivalence holds-- I just
want you to have an example in mind--
is the Lorentz model for an atom, where
you describe the atom as an electron connected
with a spring to the nucleus.
And as we will see in a few weeks,
this model gives the identical answer--
identical to the quantum mechanical treatment--
for probabilities like the polarizability
and the index of refraction for gas of atoms or molecules.
OK.
So if you have a two-level system,
you can often think we have an s, ground state, and then
p, excited state.
And if you do a weak excitation, we
have sort of a wave function, which
is all-- that's a positive 1 sine,
and then we mix the p orbital, which
has a node which is positive and negative.
And now we have the positive, negative, and the positive,
and that there is the resonant frequency between the two,
and that together results in an oscillating dipole.
So the simple model of superimposing
an s state and a p state at a certain frequency
gives us an oscillating dipole, which
is a realization of an harmonic oscillator.
But the harmonic oscillator, it oscillates.
And this is of course, valid for sufficiently small excitation.

So the question we have already addressed in the discussion--
what is small?
So small means population of higher excited states
is negligible.
So in other words, as long as the excitation of the first
excited state is small, then we can neglect the excitation
in the second excited state, which is even smaller.