My Graduate School Experience
It is easy to get carried away into abstraction as I learn about the traditional and well established physical laws. Perhaps the furthest out I got was during my Quantum Field Theory class final presentation where I addressed Ghost fields, seen here. At that point I ran in fear back to something more tangible, molecules. It turns out that molecules are still very mysterious but rich algebraic theory offers great insights. This is where I have decided to set up camp. However, I often take small tours of other fields.
- General Relativity Survey - TASI Lectures on cosmology - 2011 Nobel Prize in physics
- String Theory Survey
- Standard Model Survey - CERN reference - The actual Standard Model Lagrangian
I am most interested in reaction dynamics, and so that's what I am doing for my PhD.
A few entertaining quotes
"Classical mechanics can solve the 2-body problem but not the three-body problem (Poincare - Given a system of arbitrarily many mass points that attract each according to Newton's, under the assumption that no two points ever collide, try to find a representation of the coordinates of each point as a series in a variable that is some known function of time and for all of whose values the series converges uniformly.). So we invent…Quantum mechanics, which can solve the 1-body problem but not the 2-body problem (spooky action-at-a-distance, entanglement). So we invent…Relativistic quantum mechanics, which can solve the 0-body problem but not the 1-body problem (Dirac sea). So we invent…Quantum Field theory, which cannot solve the 0-body problem (infinite vacuum energy)" Martin C. Gutzwiller
"However, in general terms, ID is not a scientific theory, and therefore has no place in a science class room. Consider, for example, gravity and the other fundamental forces. One could say, "Science has no explanation for where gravity comes from and why it is so weak, thus allowing it to dominate on cosmic scales, make stars and planets and so forth. Maybe an intelligent designer picked all the force coupling constants". The answer could well be that that is the case, but that would give no insight into how it gravity or the other forces work. It adds nothing to the science of physics, and so is "useless" as a conjecture. It would be pointless to modify a science curriculum to say, "God created Gravity". The science of biology has to deal with empirical evidence just like all other science. It is too bad that people get testy over ID, but wouldn't you get mad if at some future date you had to teach a course on general relativity that included the addendum, "Gravity's weakness can also be understood as being deliberate instituted by the Buddha"?" Phil Matheson
Focal points of my dissertation
- Natural coordinates
- Potential energy surfaces
- Stationary states
- Dynamic quantum states
Molecular Collision Theory
Reaction dynamics is a field where approximation methods flourish. However, algebraic methods can be used to construct a Hamiltonian such that one may avoid differential operators and/or wave functions, thus avoid approximations. The familiar ladder operator form of the harmonic oscillator Hamiltonian is an example of this using a Lie algebra. When approaching molecular dynamics with this method the calculations become cleaner. A more common procedure, perturbation theory, results in an infinite amount of differential equations while the algebraic approach sustains analyticity with a finite amount of equations. However, the equations are coupled and nonlinear. To calculate dynamics of many atom systems, approximations are essential. Perhaps the most common approach is the Born-Oppenheimer Approximation. For processes with no electron transfer this method is analogous to the adiabatic theorem in that the nuclei move much slower than the electrons. The energy eigenvalue othe resulting equation is a function of the "parametrized" nuclear coordinates. This is considered the potential energy surface for the nuclei. This surface is available from electronic structure calculations or obtained by some semiempirical or emperical method. With this surface, reactions between different molecular species can be visualized intuitively. An important detail of these reactions is seen when different types of energy are transferred/exchanged during the scattering process...continue