REPORTSThese reports are pre-thesis studies related to various research projects and courses taken. More recent work can be found in the thesis. |
Mathematics of Neuroscience
Neurons can be described using nonlinear dynamical techniques.
A compilation of my homework reports and final report for a
class I took at Drexel (Math 723) with Dr. Medvedev can be
found here. A number of MATLAB,
C++, and Maple programs for dynamical computations are included.
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DecoherenceIs Quantum Decoherence the von Neumann wave collapse? An oral qualifier report can be read here. PDF version |
Master Equation
A detailed derivation of the quantum optics master equation
collected from many sources
and including steps not often found elsewhere is found
here. |
Mathieu's Equations
A detailed look at these important equations
is found here. |
Successive (simultaneous) Overrelaxation
A useful presentation on this numerical method is found
here. |
Quantization of the Harmonic Oscillator
Though found in many text books, we present a derivation with
more detail than typical
here. |
Quantum Mechanics of Hydrogen
Shown in more detail than typical, the basic
equations for the hydrogen atom are derived
here.
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Aufbau Principal and Selection Rules
An incomplete look at Rydberg atoms (to be finished in time) is
here. |
Electronic Shell Periodic Table (2006) |
Collected derivation of Stirling's equationI had trouble finding a derivation of Stirling's equation that was thorough and collected, so I ran through some of my text books and collected a cogent single stranded derivation here. |
The Pfaffian and the Wedge Product
Via proofs from Thomas Muir and S. Parameswaran, we remind the reader
of the relationship between the Pfaffian and Determinant for for a
zero-axis skew symmetric matrix. This is done in the context of a
wedge product example and can be found
here.
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