Quantum mechanics for electrical engineers - Sullivan, Dennis Michael 1949- (Hoboken, N.J. Wiley, 2012)
Introduction -- Why quantum mechanics? -- Simulation of the one-dimensional, time-dependent Schrödinger equation -- Physical parameters: the observables -- The potential V(x) -- Propagating through potential barriers -- Stationary states -- The infinite well -- Eigenfunction decomposition -- Periodic boundary conditions -- Eigenfunctions for arbitrarily shaped potentials -- Coupled wells -- Bra-ket notation -- Fourier theory in quantum mechanics -- The Fourier transform -- Fourier analysis and available states -- Uncertainty -- Transmission via FFT -- Matrix algebra in quantum mechanics -- Vector and matrix representation -- Matrix representation of the Hamiltonian -- The eigenspace representation -- Formalism -- A brief introduction to statistical mechanics -- Density of states -- Probability distributions -- The equilibrium distribution of electrons and holes -- The electron density and the density matrix -- Bands and subbands -- Bands in semiconductors -- The effective mass -- Modes (subbands) in quantum structures -- The Schrödinger equation for spin-1/2 fermions -- Spin in fermions -- An electron in a magnetic field -- A charged particle moving in combined E and B fields -- The Hartree-Fock approximation -- The Green's function formulation -- Introduction -- The density matrix and the spectral matrix -- The matrix version of the Green's function -- The self-energy matrix -- Transmission -- The single-energy channel -- Current flow -- The transmission matrix -- Conductance -- Büttiker probes -- A simulation example -- Approximation methods -- The variational method -- Non-degenerate perturbation theory -- Degenerate perturbation theory -- Time-dependent perturbation theory -- The harmonic oscillator -- The harmonic oscillator in one dimension -- The coherent state of the harmonic oscillator -- The two-dimensional harmonic oscillator -- Finding eigenfunctions using time-domain simulation -- Finding the eigenenergies and eigenfunctions in one-dimension -- Finding the eigenfunctions of two-dimensional structures -- Finding a complete set of eigenfunctions -- Appendix A. important constants and units -- Appendix B. Fourier analysis and the fast Fourier transform (FFT) -- Appendix C. an introduction to the Green's function method -- Appendix D. listings of programs used in this book
Includes bibliographical references and index.
Keywords: Electrical enginnering; Quantum theory; Electricity