Quantum Mechanics of Charged Particle Beam Optics: Understanding Devices from Electron Microscopes to Particle Accelerators

Description

Classical Charged Particle Beam Optics used in the design and operation of all present-day charged particle beam devices, from low energy electron microscopes to high energy particle accelerators, is entirely based on classical mechanics. A question of curiosity is: How is classical charged particle beam optics so successful in practice though the particles of the beam, like electrons, are quantum mechanical? Quantum Mechanics of Charged Particle Beam Optics answers this question with a comprehensive formulation of 'Quantum Charged Particle Beam Optics' applicable to any charged particle beam device. Cover Half Title Series Page Title Page Copyright Page Dedication Contents Preface Authors Chapter 1 Introduction Chapter 2 An Introductory Review of Classical Mechanics 2.1 Single Particle Dynamics 2.1.1 Lagrangian Formalism 2.1.1.1 Basic Theory 2.1.1.2 Example: Motion of a Charged Particle in an Electromagnetic Field 2.1.2 Hamiltonian Formalism 2.1.2.1 Basic Theory 2.1.2.2 Example: Motion of a Charged Particle in an Electromagnetic Field 2.1.3 Hamiltonian Formalism in Terms of the Poisson Brackets 2.1.3.1 Basic Theory 2.1.3.2 Example: Dynamics of a Charged Particle in a Constant Magnetic Field 2.1.4 Changing the Independent Variable 2.1.4.1 Basic Theory 2.1.4.2 Example: Dynamics of a Charged Particle in a Constant Magnetic Field 2.1.5 Canonical Transformations 2.1.5.1 Basic Theory 2.1.5.2 Optical Hamiltonian of a Charged Particle Moving Through an Electromagnetic Optical Element with a Straight Axis 2.1.6 Symplecticity of Canonical Transformations 2.1.6.1 Time-Independent Canonical Transformations 2.1.6.2 Time-Dependent Canonical Transformations: Hamiltonian Evolution 2.1.6.3 Canonical Invariants: Poisson Brackets 2.2 Dynamics of a System of Particles Chapter 3 An Introductory Review of Quantum Mechanics 3.1 Introduction 3.2 General Formalism of Quantum Mechanics 3.2.1 Single Particle Quantum Mechanics: Foundational Principles 3.2.1.1 Quantum Kinematics 3.2.1.2 Quantum Dynamics 3.2.1.3 Different Pictures of Quantum Dynamics 3.2.1.4 Ehrenfest’s Theorem 3.2.1.5 Spin 3.3 Nonrelativistic Quantum Mechanics 3.3.1 Nonrelativistic Single Particle Quantum Mechanics 3.3.1.1 Free Particle 3.3.1.2 Linear Harmonic Oscillator 3.3.1.3 Two-Dimensional Isotropic Harmonic Oscillator 3.3.1.4 Charged Particle in a Constant Magnetic Field 3.3.1.5 Scattering States 3.3.1.6 Approximation Methods, Time-Dependent Systems, and the Interaction Picture 3.3.1.7 Schrödinger–Pauli Equation for the Electron 3.3.2 Quantum Mechanics of a System of Identical Particles 3.3.3 Pure and Mixed States: Density Operator 3.4 Relativistic Quantum Mechanics 3.4.1 Klein–Gordon Equation 3.4.1.1 Free-Particle Equation and Difficulties in Interpretation 3.4.1.2 Feshbach–Villars Representation 3.4.1.3 Charged Klein–Gordon Particle in a Constant Magnetic Field 3.4.2 Dirac Equation 3.4.2.1 Free-Particle Equation 3.4.2.2 Zitterbewegung 3.4.2.3 Spin and Helicity of the Dirac Particle 3.4.2.4 Spin Magnetic Moment of the Electron and the Dirac–Pauli Equation 3.4.2.5 Electron in a Constant Magnetic Field 3.4.3 Foldy–Wouthuysen Transformation 3.4.3.1 Foldy–Wouthuysen Representation of the Dirac Equation 3.4.3.2 Foldy–Wouthuysen Representation of the Feshbach–Villars form of the Klein–Gordon Equation 3.5 Appendix: The Magnus Formula for the Exponential Solution of a Linear Differential Equation Chapter 4 An Introduction to Classical Charged Particle Beam Optics 4.1 Introduction: Relativistic Classical Charged Particle Beam Optics 4.2 Free Propagation 4.3 Optical Elements with Straight Optic Axis 4.3.1 Axially Symmetric Magnetic Lens: Imaging in Electron Microscopy 4.3.2 Normal Magnetic Quadrupole 4.3.3 Skew Magnetic Quadrupole 4.3.4 Axially Symmetric Electrostatic Lens 4.3.5 Electrostatic Quadrupole 4.4 Bending Magnet: An Optical Element with a Curved Optic Axis 4.5 Nonrelativistic Classical Charged Particle Beam Optics Chapter 5 Quantum Charged Particle Beam Optics: Scalar Theory for Spin-0 and Spinless Particles 5.1 General Formalism of Quantum Charged Particle Beam Optics 5.2 Relativistic Quantum Charged Particle Beam Optics Based on the Klein–Gordon Equation 5.2.1 General Formalism 5.2.2 Free Propagation: Diffraction 5.2.3 Axially Symmetric Magnetic Lens: Electron Optical Imaging 5.2.3.1 Paraxial Approximation: Point-to-Point Imaging 5.2.3.2 Going Beyond the Paraxial Approximation: Aberrations 5.2.3.3 Quantum Corrections to the Classical Results 5.2.4 Normal Magnetic Quadrupole 5.2.5 Skew Magnetic Quadrupole 5.2.6 Axially Symmetric Electrostatic Lens 5.2.7 Electrostatic Quadrupole Lens 5.2.8 Bending Magnet 5.3 Effect of Quantum Uncertainties on Aberrations in Electron Microscopy and Nonlinearities in Accelerator Optics 5.4 Nonrelativistic Quantum Charged Particle Beam Optics: Spin-0 and Spinless Particles 5.5 Appendix: Propagator for a System with Time-Dependent Quadratic Hamiltonian Chapter 6 Quantum Charged Particle Beam Optics: Spinor Theory for Spin-1/2 Particles 6.1 Relativistic Quantum Charged Particle Beam Optics Based on the Dirac–Pauli Equation 6.1.1 General Formalism 6.1.1.1 Free Propagation: Diffraction 6.1.1.2 Axially Symmetric Magnetic Lens 6.1.1.3 Bending Magnet 6.1.2 Beam Optics of the Dirac Particle with Anomalous Magnetic Moment 6.1.2.1 General Formalism 6.1.2.2 Lorentz and Stern–Gerlach Forces, and the Thomas–Frenkel–BMT Equation for Spin Dynamics 6.1.2.3 Phase Space and Spin Transfer Maps for a Normal Magnetic Quadrupole 6.1.2.4 Phase Space and Spin Transfer Maps for a Skew Magnetic Quadrupole 6.2 Nonrelativistic Quantum Charged Particle Beam Optics: Spin-1/2 Particles Chapter 7 Concluding Remarks and Outlook on Further Development of Quantum Charged Particle Beam Optics Bibliography Index