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Introduction to Quantum Nanotechnology

A Problem Focused Approach

Duncan G. Steel

April 2021

ISBN: 9780192895073

400 pages
Hardback
246x189mm

In Stock

Price: £65.00

This book serves as introduction to quantum theory with emphasis on dynamical behaviour and applications of quantum mechanics, with minimal discussion of formalism. The goal is to help engineering and physics students begin to learn the tools for a quantum toolbox they will need to work in this area.

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Description

This book serves as introduction to quantum theory with emphasis on dynamical behaviour and applications of quantum mechanics, with minimal discussion of formalism. The goal is to help engineering and physics students begin to learn the tools for a quantum toolbox they will need to work in this area.

  • Introduces undergraduates to ideas and material often not seen until semester 2 or 3 in graduate school
  • Enables students to feel they are really part of the quantum revolution and building a quantum toolbox
  • Includes problems for students as an integral part of the presentation
  • Covers two semesters of content but offers multiple one-semester options

About the Author(s)

Duncan G. 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 Schrödinger 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 Göpert-Mayer Transformation
    E:The Electromagnetic Hamiltonian and the Göpert-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.

Reviews

"This book presents a combination of quantum physics and nanotechnology which is appealing and quite distinctive. The author has a huge amount of experience in presenting the material in the book to an undergraduate audience, and in working with the same range of ideas in a research context. The nature of the presentation of the material reflects this experience." - Richard Phillips, University of Cambridge

"Duncan Steel has written an excellent textbook for intermediate engineering students, based on his experience in teaching classes in the area of quantum mechanics for engineers and in mentoring research students in the basic physics issues in quantum technology. His selection of topics is right on the mark. His consideration for the accessibility by the students is detailed, valuable and quite rare. The book has a lot of appeal. " - Lu J. Sham, University of California at San Diego