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 300 K = 1/40 eV which is apparently critical to many researchers in this field. At 13.58 eV, H is ionized and more atoms become ionized in the tens and hundreds of eVs. At around 1keV, the inner shell electrons begin to be effected, and at 100 keV-1 MeV, the nucleus begins to experience the energy. As the energy increases from there, we can get into particles within the nucleus being effected and eventually get down to the quark scale.
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 Maxwellís 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 Iím 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 SchrŲdingerís 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. Iím 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 SchrŲdingerís 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 SchrŲdingerís 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 SchrŲdingerís 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, Iím still new to most of the particles we were talking about, such as the muons and neutrinos. I donít 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 werenít 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. Machís philosophy was that if we had no way of observing, even with calculation, such atoms, then in the eyes of physics, they donít 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 Avogadroís 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 donít 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 wasnít there, people would continue on believing in atoms and eventually face problems later on down the road. I also liked talking about Loschmidtís 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.