**
**First
off, Dr. Weaver is in charge of the REU program at KSU and is incredibly
knowledgeable and helpful. He offers to give assistance to all of the students
and their projects, even though many of them are quite diverse and hard to
follow to somebody not directly researching them. It would most likely not be
the same experience without him, or Dr. Kristan Corwin, who is his second in
command. About once or twice a week, the students are able to hear relevant
lectures from Dr. Weaver, and here are some general overviews of them.

** **

__Energy Scales__**:
5/27**

**
**Since
many of us will be working on the atomic level, the electron-volt was described
to us very in depth and we were given a feel for when certain physical and
chemical processes occur in reference to this energy unit. The general
conversion was introduced that

This is the first time the eV has been put in a somewhat practical perspective for me. I had learned about them more in depth from Modern Physics, but it was not explained in terms of interactions of particles and I could not always gage when my answer would be too high or low in the scale. I now feel as if I have a higher understanding of these still somewhat foreign units, but I feel I will be more comfortable with them as time goes on.

__Waves and Lasers__**:
5/30/08**

**
**The
core of how lasers work was gone over during this session, starting with
Maxwell’s Equations and why electric fields are used in determining
polarization direction over magnetic fields and then diving into an analysis of
electric fields to understand why a laser functions. From the lecture, it was
shown that a resonator with mirrors on the sides is used to contain atoms that
become excited, and then give off coherent light that (almost) perfectly
constructively interferes with itself as it bounces in between the mirrors. An
expression for the final e-field that leaves as a function of the translation
and reflection coefficients, as well as the incident e-field, index of
refraction of light, length of the resonator, and gain from the mirrors. At the
end, it was proven that the light must move at integer multiples of a threshold
angular frequency in order for the laser to work.

The lecture was very similar to one I had earlier this year in my Physical
Optics class, which is considered an introduction to optical phenomena. It was
enjoyable to be able to fully comprehend the material that was review as well
as the topics that were covered in more depth than before. Since I’m an Optics
double degree, I felt like I got a lot out of hearing the lecture and was able
to solidify my basic knowledge of how the laser works.

__Atoms
and Molecules__**:
6/3**

** **The relationship
between classical and quantum mechanics was looked into, first with a brief analysis
of a rotator, and then with a harmonic oscillator. The concepts of operators
were also introduced, mainly the Hamiltonian operator, as well as eigenvalues
and eigenfunctions. For example, it was told that the quantum expression for
energy is simply the eigenvalue of the Hamiltonian operator. Then the mechanics
of a molecule was described, starting with the total energy it has due to
kinetic and effective potential energy. We then discussed the magnitude that
each energy has as well as how much energy goes into the vibration and rotation
of the molecules, with rotation needing much more energy than simply vibration.
Due to the fact that the molecules do vibrate, we also developed a relationship
between the spring constant and said molecules.

I
just started learning about quantum mechanics this year, having discussions
about it in Modern Physics. This lecture helped reinforce the idea that energy
and momenta are quantized and how they result from Schrödinger’s Equation. We
also talked about the importance of the wave function, which I find to be very
fascinating since it is the best description of how things will react on a
quantum level, but can only give a probability of each outcome. I’m very
interested in learning about this branch of physics more in depth in the future
and also possibly studying when and why the equations/rules on the quantum
scale break down for the classical approach.

__Superposition:
From Rabi oscillations to neutrino oscillations__**: 6/5**

** **The lecture
started out with defining what it meant by saying the Hamiltonian is a linear
operator, mainly that solutions to the equation found make another solution in
the form of a linear combination. The main topic of the discussion would be
situations where there are only two such solutions or states that can be added
together in order to solve Schrödinger’s Equation and find the appropriate wave
function.

The
first topic was quantum beat spectroscopy. It was told that light can excite
the particle of interest into one of our two excited states, and then it will
eventually go down into a fluorescent state by emitting a lower energy photon.
To find the amplitude of such a condition, we would need a decay operator and
have to find expectation values for said amplitude. It was shown that the final
solution produced what would be expected in a simple double slit diffraction
experiment.

Next
we talked about Rabi Oscillations. This dealt with the two possible states
being stimulated by an oscillating electric field. Using Schrödinger’s equation
again, two equations were found that related the energy of the states to an
electric dipole moment that was dotted into the electric field. The key to such
oscillations was shown when these equations were broken down into exponentials,
one which would oscillate very quickly, which has little effect on the system,
and the other would go slowly. The quicker one is assumed to be zero, and the
analysis was carried out further until solutions were found.

Finally,
the topic of neutrino oscillations was briefly mentioned. We saw that the two
different neutrino energy states could be used in a linear combination to form
either antimatter electron neutrinos or antimatter muon neutrinos. Later, Dr.
Weaver mentioned that due to their oscillations, the electron neutrino can
break down into muon neutrinos. It was also said that when these antimatter
neutrinos, they can change into their matter counterparts. Electron neutrinos
can become electrons.

This
lecture was more out of my grasp than the others. The analysis of Schrödinger’s
equation for the different cases made since, but I would like to go back and
see if I can get the math to work out myself, along with the initial conditions
provided. Also, I’m still new to most of the particles we were talking about,
such as the muons and neutrinos. I don’t really know where they come from or
what their significance is, so it was difficult to grasp the importance of the
calculations made during the lecture.

__Cross-sections:
Are Atoms Real?__**:
6/10**

** **The talk on this
day had a little mix of science, history, and philosophy. It began with the
1800s when people weren’t sure if atoms actually existed or not. Chemists were
on the believing side since the assumptions greatly simplified and explained
many chemical processes. However, many physicists, such as Mach, were very
skeptical. Mach’s philosophy was that if we had no way of observing, even with
calculation, such atoms, then in the eyes of physics, they don’t exist. This
was a reference to the fact that nobody knew how big atoms were or how many
there were in a given amount of substance. Chemists had already developed the
concept of a mole, but did not know Avogadro’s number. This skepticism is still
prevalent today with the study of quarks and antiquarks.

Then
the discussion went into how one scientist, Loschmidt, set out to actually
measure their size, and thus proving their existence. As a background, Dr.
Weaver went into the idea of particles hitting a surface and finding out how
many there were using the idea of cross-sections and flux. This eventually led
him to creating a differential equation, which would model gasses traveling
through space and how their numbers would dwindle as we moved further down this
space, as Loschmidt did. Eventually, we learned that he was able to compress
that gas into a liquid and measured its volume to approximate the volume of the
gas and then this led him to calculate the size and number of atoms in that
sample, assuming they were hard spheres.

Finally,
we got to this idea using Coulomb forces, as Rutherford did to try and explain
the results of his Gold Foil Experiment. He simulated a very light charged
particle (an electron) coming near a very heavy particle (a nucleus) and
studied the deflection of the light particle using conservation of momentum and
finding a differential cross-section. Dr. Weaver then let us know, for this
particular force, if we approached it from a quantum mechanics point of view,
treating the electron as a diffracting wave, the exact same result is found for
the cross-section.

For
me, the talk was very intriguing and showed us a lot about the mind of a
scientist. The discussion about Mach and his inability to believe without proof
shows the skepticism scientists must have when new ideas come up. Although he
ended being wrong in the fact that atoms don’t exist, it was necessary to
require some proof of their existence. If atoms were not real, then this
skepticism would have eventually led somebody to disprove their existence, but
if the skepticism wasn’t there, people would continue on believing in atoms and
eventually face problems later on down the road. I also liked talking about
Loschmidt’s method of determining the size of an atom. That shows the creative
side of scientists and how they must think outside the box in order to perform
the calculations or find the values they want. Overall, there are a lot more to
scientists than lab coats and complex calculations.

__Energy
Levels in the Hydrogen Atom__**:6/19**

** **This talk involved
going in depth with the idea of energy levels with the hydrogen atom beyond the
normal s,p,d levels. This involved going
into the different quantum numbers and showing their significance. Using 2s, 2
would be n, which tells about the size of the orbital, and s represents l=0,
ans p is l=1, d is l=2, etc. It was later discussed that this value is part of
the expression for angular momentum.

When
then shifted gears a little, and went into what would happen if we observed
these states from different coordinate systems. The conclusion would be that
what it would be a superposition of all the possible states in the first
reference frame, which is the same idea of rotating even simple objects.

The
lecture ended with the concept of spin, the two state system, and how it
further effects the separations of the energy levels. Combining this with the
other quantum levels, we were shown how many other states were formed and the
specific energy levels they form. Eventually, we went into the Fine Structure,
made by Dirac.