MARC CAHAY, Spintronics and Vacuum Nanoelectronics Laboratory, University of Cincinnati, USA SUPRIYO BANDYOPADHYAY, School of Engineering, Virginia Commonwealth University, USA

• About the Authors ixPreface xi1 General Properties of the Schrodinger Equation 12 Operators 153 Bound States 474 Heisenberg Principle 805 Current and Energy Flux Densities 1016 Density of States 1287 Transfer Matrix 1668 Scattering Matrix 2059 Perturbation Theory 22810 Variational Approach 24511 Electron in a Magnetic Field 26112 Electron in an Electromagnetic Field and Optical Properties of Nanostructures 28113 Time-Dependent Schrodinger Equation 292A Postulates of Quantum Mechanics 314B Useful Relations for the One-Dimensional Harmonic Oscillator 317C Properties of Operators 319D The Pauli Matrices and their Properties 322E Threshold Voltage in a High Electron Mobility Transistor Device 325F Peierls’s Transformation 329G Matlab Code 332Index 343

MARC CAHAY, Spintronics and Vacuum Nanoelectronics Laboratory, University of Cincinnati, USA SUPRIYO BANDYOPADHYAY, School of Engineering, Virginia Commonwealth University, USA

• About the Authors ixPreface xi1 General Properties of the Schrodinger Equation 12 Operators 153 Bound States 474 Heisenberg Principle 805 Current and Energy Flux Densities 1016 Density of States 1287 Transfer Matrix 1668 Scattering Matrix 2059 Perturbation Theory 22810 Variational Approach 24511 Electron in a Magnetic Field 26112 Electron in an Electromagnetic Field and Optical Properties of Nanostructures 28113 Time-Dependent Schrodinger Equation 292A Postulates of Quantum Mechanics 314B Useful Relations for the One-Dimensional Harmonic Oscillator 317C Properties of Operators 319D The Pauli Matrices and their Properties 322E Threshold Voltage in a High Electron Mobility Transistor Device 325F Peierls’s Transformation 329G Matlab Code 332Index 343

MARC CAHAY, Spintronics and Vacuum Nanoelectronics Laboratory, University of Cincinnati, USA SUPRIYO BANDYOPADHYAY, School of Engineering, Virginia Commonwealth University, USA

• About the Authors ixPreface xi1 General Properties of the Schrodinger Equation 12 Operators 153 Bound States 474 Heisenberg Principle 805 Current and Energy Flux Densities 1016 Density of States 1287 Transfer Matrix 1668 Scattering Matrix 2059 Perturbation Theory 22810 Variational Approach 24511 Electron in a Magnetic Field 26112 Electron in an Electromagnetic Field and Optical Properties of Nanostructures 28113 Time-Dependent Schrodinger Equation 292A Postulates of Quantum Mechanics 314B Useful Relations for the One-Dimensional Harmonic Oscillator 317C Properties of Operators 319D The Pauli Matrices and their Properties 322E Threshold Voltage in a High Electron Mobility Transistor Device 325F Peierls’s Transformation 329G Matlab Code 332Index 343