About the Authors ix

Preface xi

1 General Properties of the Schrodinger Equation 1

2 Operators 15

3 Bound States 47

4 Heisenberg Principle 80

5 Current and Energy Flux Densities 101

6 Density of States 128

7 Transfer Matrix 166

8 Scattering Matrix 205

9 Perturbation Theory 228

10 Variational Approach 245

11 Electron in a Magnetic Field 261

12 Electron in an Electromagnetic Field and Optical Properties of Nanostructures 281

13 Time-Dependent Schrodinger Equation 292

A Postulates of Quantum Mechanics 314

B Useful Relations for the One-Dimensional Harmonic Oscillator 317

C Properties of Operators 319

D The Pauli Matrices and their Properties 322

E Threshold Voltage in a High Electron Mobility Transistor Device 325

F Peierls’s Transformation 329

G Matlab Code 332

Index 343

PROBLEM SOLVING IN QUANTUM MECHANICS

FROM BASICS TO REAL-WORLD APPLICATIONS FOR MATERIALS

SCIENTISTS, APPLIED PHYSICISTS, AND DEVICES ENGINEERS

This topical and timely textbook is a collection of problems for students, researchers, and practitioners interested in state-of-the-art material and device applications in quantum mechanics. Most problem are relevant either to a new device or a device concept or to current research topics which could spawn new technology. It deals with the practical aspects of the field, presenting a broad range of essential topics currently at the leading edge of technological innovation.

Includes discussion on:

• Properties of Schrödinger Equation
• Operators
• Bound States in Nanostructures
• Current and Energy Flux Densities in Nanostructures
• Density of States
• Transfer and Scattering Matrix Formalisms for Modelling Diffusive Quantum Transport
• Perturbation Theory, Variational Approach and their Applications to Device Problems
• Electrons in a Magnetic or Electromagnetic Field and Associated Phenomena
• Time-dependent Perturbation Theory and its Applications
• Optical Properties of Nanostructures

Problem Solving in Quantum Mechanics: From Basics to Real-World Applications for Materials Scientists, Applied Physicists, and Devices Engineers is an ideal companion to engineering, condensed matter physics or materials science curricula. It appeals to future and present engineers, physicists, and materials scientists, as well as professionals in these fields needing more in-depth understanding of nanotechnology and nanoscience.