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.

1 General Properties of the Schrödinger 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 Schrödinger 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

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