Quantum Mechanics for Electrical Engineers / IEEE Press Series on Microelectronic Systems (ePub)

1. Introduction 1.1 Why Quantum Mechanics 1.2 Simulation of the One-Dimensional, Time-Dependent Schrödinger Equation 1.3 Physical Parameters-the Observables 1.4 The Potential V(X) 1.5 Propagating Through Potential Barriers 1.6 Summary 2. Stationary States 2.1 The Infinite Well 2.2 Eigenfunction Decomposition 2.3 Periodic Boundary Conditions 2.4 Eigenfunctions for Arbitrarily Shaped Potentials 2.5 Coupled Wells 2.6 Bra-ket Notation 2.7 Summary. 3. Fourier Theory in Quantum Mechanics 3.1 The Fourier Transform 3.2 Fourier Analysis and Available States 3.3 Uncertainty 3.4 Transmission via FFT 3.5 Summary 4. Matrix Algebra in Quantum Mechanics 4.1 Vector and Matrix Representation 4.2 Matrix Representation of the Hamiltonian 4.3 The Eigenspace Representation 4.4 Formalism 5. Statistical Mechanics 5.1 Density of States 5.2 Probability Distributions 5.3 The Equilibrium Distribution of Electrons and Holes 5.4 The Electron Density and the Density Matrix 6. Bands and Subbands 6.1 Bands in Semiconductors 6.2 The Effective Mass 6.3 Modes (Subbands) in Quantum Structures 7. The Schrödinger Equation for Spin-1.2 Fermions 7.1 Spin in Fermions 7.2 An Electron in a Magnetic Field 7.3 A Charged Particle Moving in Combined E and B fields 7.4 The Hartree-Fock Approximation 8. Green's Functions Formulation 8.1 Introduction 8.2 The Density Matrix and the Spectral Matrix 8.3 The Matrix Version of the Green's Function 8.4 The Self-Energy Matrix 9. Transmission 9.1 The Single-Energy Channel 9.2 Current Flow 9.3 The Transmission Matrix 9.4 Conductance 9.5 Büttiker probes 9.6 A Simulation Example 10. Approximation Methods 10.1 The Variational Method 10.2 Non-Degenerate Perturbation Theory 10.3 Degenerate Perturbation Theory 10.4 Time-Dependent Perturbation Theory 11. The Harmonic Oscillator 11.1 The Harmonic Oscillator in One Dimension 11.2 The Coherent State of the Harmonic Oscillator 11.3 The Two-Dimensional Harmonic Oscillator 12. Finding Eigenfunctions Using Time-Domain Simulation 12.1

DENNIS M. SULLIVAN is Professor of Electrical and Computer Engineering at the University of Idaho as well as an award-winning author and researcher. In 1997, Dr. Sullivan's paper "Z Transform Theory and FDTD Method" won the IEEE Antennas and Propagation Society's R. P. W. King Award for the Best Paper by a Young Investigator. He is the author of Electromagnetic Simulation Using the FDTD Method.

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