Finite Elements in Action Modeling Quantum Mechanics and Electrodynamics in Nanoscale Systems

L. Ramdas Ram-Mohan, Director, Center for Computational NanoScience (CCNS), Worcester Polytechnic Institute

L. Ramdas Ram-Mohan graduated from St. Stephen's College at Delhi University with a B.Sc. (Honors) in 1964 and did his graduate work at Purdue University in theoretical high energy physics earning his MS and PhD in 1971. After post-doctoral assignments at the Freie Universität in Berlin and Delhi University, he joined Purdue University from 1975 to 1978. He has been at Worcester Polytechnic Institute since 1978 as Assistant, Associate, and was made Full Professor in 1985. His interests have ranged from quantum field theory, linear and nonlinear optical properties of semiconductor heterostructures, to high-accuracy finite element methods for scattering theory and electrodynamics, band structures of solids, and wavefunction engineering of quantum well lasers.

Part I - The Action Integral in Quantum Mechanics1. Schrödinger's equation and the action2. Action, FEM and BCs3. Element geometries for 2D and 3D4. Boundary conditions at material interfaces5. Accidental degeneracy in cubic semiconductor quantum dotsPart II - Quantum Scattering6. Quantum scattering in 1D revisited7. 2D quantum waveguides8. Quantum scattering in 2D waveguides9. Open domain quantum scattering with sources and absorbersPart III - Wavefunction Engineering10. Wavefunction engineering of semiconductor nanostructures11. Schrödinger-Poisson self-consistency in layered semiconductor nanostructuresPart IV - Steady-state current distributions12. The Extraordinary Magneto-Resistance effect in metal- semiconductor structures13. Read-head design based on the EMR effectPart V - Electrodynamics14. Fields in electromagnetic waveguides15. Modeling photonic crystals with Hermite FEM16. Cavity Electrodynamics and symmetries17. Dimensional continuation of EM singularities in structures with re-entrant geometry18. The gauge degree of freedom in ElectrodynamicsPart VI - Further applications of FEMA. Derivation of shape functions using group theoryB. Shape functions for 1D, 2D, and 3D finite elementsC. Hermite Least Squares Data Fitting