## Author Biography

Duncan Steel, *Professor of Electrical Engineering and Computer Science, Professor of Physics, University of Michigan*

Duncan G. Steel, The Robert J. Hiller Professor, Professor of Electrical Engineering and Computer Science, Professor of Physics, The University of Michigan - Ann Arbor. PhD in 1976 in Electrical and Nuclear Science, University of Michigan. Guggenheim Fellow (1999), APS Isakson Prize (2010), Elected Fellow of APS, OSA, and IEEE. 10 years at Hughes Research Laboratories (senior staff physicist), faculty at the University of Michigan (1985-), Area Chair for Optics and Director of the Optical Sciences Laboratory 1988-2007, Director of Biophysics 2007-2009.

## Table of Contents

**Chapter 1. Introduction to Applied Quantum Mechanics - Why quantum behavior is impacting technology. **

**Chapter 2. Nano Mechanical Oscillator and Basic Dynamics: Part I **

2.1. Introduction

2.2. The Classical Approach: Finding

2.3. The Quantum Approach: Finding

2.4. Is it Classical or Quantum?

2.5. What is Knowable in a Quantum System?

2.6. Coherent Superposition States and Coherent Dynamics

2.7. The Particle and the Wave

2.8. Summary

**Chapter 3. Free Particle, Wave Packet and Dynamics, Quantum Dots and Defects/Traps Scattering and Transport. **

3.1. Introduction

3.2. The Free Particle

3.3. Localized State in Free Space: The Wave Packet

3.4. Nano-Heterostructures: Quantum Dots and Deep Traps

3.5. A Particle Trapped in a Shallow Defect

3.6. A Particle Trapped in a Point Defect Represented by a Dirac Delta-Function Potential

3.7. Physical Interpretation of the Dirac -function potential

3.8. Summary

**Chapter 4. Periodic Hamiltonians and the Emergence of Band Structure: The Bloch Theorem and the Dirac Kronig-Penney model. **

4.1. Introduction

4.2. The Translation Operator

4.3. Crystals and Periodic Potentials: The Bloch Theorem and the Dirac Kronig-Penney Model

4.4. Summary

**Chapter 5. Scattering, Quantum Current, and Resonant Tunneling **

5.1. Introduction

5.2. Scattering

5.3. Tunneling Through a Repulsive Point Defect Represented by a Dirac -Function Potential

5.4. Resonant Tunneling

5.5. Summary

**Chapter 6. Bound States in 3-dimensions: The Atom. **

6.1. Introduction

6.2. The Hydrogenic Atom

6.3. Summary

**Chapter 7. The New Design Rules for Quantum: The Postulates. **

7.1. Introduction

7.2. The Postulates of Quantum Mechanics

7.3. The Heisenberg Uncertainty Principle: The Minimum Uncertainty State

7.4. Interpreting the Expansion Coefficients: Relating Functional Form to Dirac Form

7.5. Summary

**Chapter 8. Heisenberg Matrix Approach: Nano-Mechanical Oscillator and the Quantum LC Circuit. **

8.1. Introduction

8.2. Heisenberg or Matrix Approach to Solving the Time Independent Schr?dinger Equation

8.3. Matrix Representation of Operators and Eigenvectors in Quantum Mechanics

8.4. The Quantum LC Circuit

8.5. Summary

**Chapter 9. Quantum Dynamics: Rabi Oscillations and Quantum Flip-Flops. **

9.1. Introduction

9.2. Time Evolution Operator

9.3. The Heisenberg Picture of Dynamics

9.4. The Interaction Picture

9.5. A Quantum Flip-Flop: Coherent Control of a Two-Level System and Rabi Oscillations

9.6. Summary

**Chapter 10. The Quantum Gyroscope: The Emergence of Spin. **

10.1. Introduction

10.2. Angular Momentum with the Heisenberg Approach

10.3. Intrinsic Angular Momentum: Spin

10.4. The Bloch Sphere and Spin

10.5. Addition of Angular Momentum

10.6. Angular Momentum and the Rotation Operator

10.7. Summary

**Chapter 11. Time Independent and Time Dependent Perturbation Theory. **

11.1. Introduction

11.2. Time Independent Perturbation Theory.

11.3. Time Dependent Perturbation Theory: Fermi's Golden Rule

11.4. Summary

**Chapter 12. Bosons and Fermions: Indistinguishable particles with intrinsic spin. **

12.1. Introduction

12.2. Eigenfunctions and Eigenvalues of the Exchange Operator

12.3. The Exchange Symmetry Postulate: Bosons and Fermions

12.4. The Heitler-London Model

12.5. Summary

**Chapter 13. Quantum Measurement and Entanglement: Wave-Function Collapse **

13.1. Introduction

13.2. Quantum Measurement

13.3. Quantum Entanglement and the Impact of Measurement

13.4. Quantum Teleportation

13.5. Summary

**Chapter 14. Loss and Decoherence: The RLC Circuit **

14.1. Introduction

14.2. Coupling to a Continuum of States: The Weisskopf-Wigner Approximation

14.3. Decay in the Nano-Vibrator Problem

14.4. The RLC Circuit

14.5. Summary

**Chapter 15. The Quantum Radiation Field: Spontaneous Emission and Entangled Photons **

15.1. Introduction

15.2. Finding the Hamiltonian for the Transverse Electromagnetic Field

15.3. Quantizing the Field

15.4. Spontaneous Emission

15.5. The Effects of the Quantum Vacuum on Linear Absorption and Dispersion

15.6. Rabi Oscillations in the Vacuum: The Jaynes Cummings Hamiltonian

15.7. Summary

**Chapter 16. Atomic Operators **

16.1. Introduction

16.2. Defining the Atomic Operators

16.3. The Physical Meaning of the Atomic Operators

16.4. The Atomic Operators in the Heisenberg Picture

16.5. The Exact Solution for the Atomic Operators for a Monochromatic Field

16.6. The Operator Equations of Motion Including Spontaneous Emission

**Chapter 17. Quantum Electromagneticst **

17.1. Introduction

17.2. The Number State Representation

17.3. The Coherent State

17.4. Quantum Beam Splitter: Quantum Interference

17.5. Resonant Rayleigh Scattering: A Single Quantum Emitter

17.6. Creating a Quantum Entangled State Between a Photon and an Electron

17.7. Engineering the Quantum Vacuum

17.8. Summary

**Chapter 18. The Density Matrix: Bloch Equations **

18.1. Introduction

18.2. The Density Matrix Operator

18.3. The Density Matrix Equations Including Relaxation

18.4. Solving the Reduced Density Matrix for a Two-Level System in the Presence of Resonant Classical Electromagnetic Field

18.5. Rate Equation Approximation

18.6. The Three-Level System: Emerging Importance in Quantum Technology

18.7. Summary

**Appendices **

A. Essential Mathematics Review

B. Power Series for important Functions

C. Properties and Representations for the Dirac Delta Function

D. Vector Calculus and Vector IdentifiesThe Electromagnetic Hamiltonian and the G?pert-Mayer Transformation

E. The Electromagnetic Hamiltonian and the G?pert-Mayer Transformation

F. Maxwell's Equations in Media, the Wave Equation and Coupling to a two-level system

G. Wigner-Eckart Theorem for evaluating matrix elements.