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

  • Formāts: Hardback, 372 pages, height x width: 234x156 mm, weight: 662 g
  • Sērija : Multidisciplinary and Applied Optics
  • Izdošanas datums: 23-May-2019
  • Izdevniecība: CRC Press
  • ISBN-10: 1138035920
  • ISBN-13: 9781138035928
  • Hardback
  • Cena: 243,28 €
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  • Formāts: Hardback, 372 pages, height x width: 234x156 mm, weight: 662 g
  • Sērija : Multidisciplinary and Applied Optics
  • Izdošanas datums: 23-May-2019
  • Izdevniecība: CRC Press
  • ISBN-10: 1138035920
  • ISBN-13: 9781138035928
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.

Recenzijas

"The volume on Quantum Mechanics of Charged Particle Beam Optics by R. Jagannathan and S.A. Khan is remarkable in that the principal stages of electron optics are derived directly from Dirac's equation and some small corrections (fortunately usually negligible) to the standard theory are found. The book opens with chapters on classical mechanics, quantum mechanics, The effect of the anomalous magnetic moment is then included and sections are devoted to normal and skew quadrupoles.of interest mainly to specialists but it remains a very valuable addition to the electron optics bookshelf."

P. W. Hawkes, CEMESCNRS, France

Preface xi
Authors xv
Chapter 1 Introduction
1(8)
Chapter 2 An Introductory Review of Classical Mechanics
9(32)
2.1 Single Particle Dynamics
9(32)
2.1.1 Lagrangian Formalism
9(1)
2.1.1.1 Basic Theory
9(1)
2.1.1.2 Example: Motion of a Charged Particle in an Electromagnetic Field
10(2)
2.1.2 Hamiltonian Formalism
12(1)
2.1.2.1 Basic Theory
12(2)
2.1.2.2 Example: Motion of a Charged Particle in an Electromagnetic Field
14(2)
2.1.3 Hamiltonian Formalism in Terms of the Poisson Brackets
16(1)
2.1.3.1 Basic Theory
16(2)
2.1.3.2 Example: Dynamics of a Charged Particle in a Constant Magnetic Field
18(3)
2.1.4 Changing the Independent Variable
21(1)
2.1.4.1 Basic Theory
21(1)
2.1.4.2 Example: Dynamics of a Charged Particle in a Constant Magnetic Field
22(3)
2.1.5 Canonical Transformations
25(1)
2.1.5.1 Basic Theory
25(4)
2.1.5.2 Optical Hamiltonian of a Charged Particle Moving Through an Electromagnetic Optical Element with a Straight Axis
29(2)
2.1.6 Symplecticity of Canonical Transformations
31(1)
2.1.6.1 Time-Independent Canonical Transformations
31(1)
2.1.6.2 Time-Dependent Canonical Transformations: Hamiltonian Evolution
32(3)
2.1.6.3 Canonical Invariants: Poisson Brackets
35(1)
2.2 Dynamics of a System of Particles
36(5)
Chapter 3 An Introductory Review of Quantum Mechanics
41(132)
3.1 Introduction
41(1)
3.2 General Formalism of Quantum Mechanics
42(36)
3.2.1 Single Particle Quantum Mechanics: Foundational Principles
42(1)
3.2.1.1 Quantum Kinematics
42(9)
3.2.1.2 Quantum Dynamics
51(13)
3.2.1.3 Different Pictures of Quantum Dynamics
64(4)
3.2.1.4 Ehrenfest's Theorem
68(2)
3.2.1.5 Spin
70(8)
3.3 Nonrelativistic Quantum Mechanics
78(54)
3.3.1 Nonrelativistic Single Particle Quantum Mechanics
78(1)
3.3.1.1 Free Particle
78(12)
3.3.1.2 Linear Harmonic Oscillator
90(10)
3.3.1.3 Two-Dimensional Isotropic Harmonic Oscillator
100(3)
3.3.1.4 Charged Particle in a Constant Magnetic Field
103(4)
3.3.1.5 Scattering States
107(4)
3.3.1.6 Approximation Methods, Time-Dependent Systems, and the Interaction Picture
111(6)
3.3.1.7 Schrodinger-Pauli Equation for the Electron
117(2)
3.3.2 Quantum Mechanics of a System of Identical Particles
119(7)
3.3.3 Pure and Mixed States: Density Operator
126(6)
3.4 Relativistic Quantum Mechanics
132(38)
3.4.1 Klein-Gordon Equation
132(1)
3.4.1.1 Free-Particle Equation and Difficulties in Interpretation
132(5)
3.4.1.2 Feshbach-Villars Representation
137(2)
3.4.1.3 Charged Klein-Gordon Particle in a Constant Magnetic Field
139(2)
3.4.2 Dirac Equation
141(1)
3.4.2.1 Free-Particle Equation
141(8)
3.4.2.2 Zitterbewegung
149(1)
3.4.2.3 Spin and Helicity of the Dirac Particle
150(3)
3.4.2.4 Spin Magnetic Moment of the Electron and the Dirac-Pauli Equation
153(1)
3.4.2.5 Electron in a Constant Magnetic Field
154(2)
3.4.3 Foldy-Wouthuysen Transformation
156(1)
3.4.3.1 Foldy-Wouthuysen Representation of the Dirac Equation
156(12)
3.4.3.2 Foldy-Wouthuysen Representation of the Feshbach-Villars form of the Klein-Gordon Equation
168(2)
3.5 Appendix: The Magnus Formula for the Exponential Solution of a Linear Differential Equation
170(3)
Chapter 4 An Introduction to Classical Charged Particle Beam Optics
173(40)
4.1 Introduction: Relativistic Classical Charged Particle Beam Optics
173(1)
4.2 Free Propagation
174(4)
4.3 Optical Elements with Straight Optic Axis
178(28)
4.3.1 Axially Symmetric Magnetic Lens: Imaging in Electron Microscopy
178(19)
4.3.2 Normal Magnetic Quadrupole
197(5)
4.3.3 Skew Magnetic Quadrupole
202(2)
4.3.4 Axially Symmetric Electrostatic Lens
204(1)
4.3.5 Electrostatic Quadrupole
205(1)
4.4 Bending Magnet: An Optical Element with a Curved Optic Axis
206(4)
4.5 Nonrelativistic Classical Charged Particle Beam Optics
210(3)
Chapter 5 Quantum Charged Particle Beam Optics: Scalar Theory for Spin-0 and Spinless Particles
213(74)
5.1 General Formalism of Quantum Charged Particle Beam Optics
213(1)
5.2 Relativistic Quantum Charged Particle Beam Optics Based on the Klein-Gordon Equation
214(63)
5.2.1 General Formalism
214(16)
5.2.2 Free Propagation: Diffraction
230(2)
5.2.3 Axially Symmetric Magnetic Lens: Electron Optical Imaging
232(1)
5.2.3.1 Paraxial Approximation: Point-to-Point Imaging
232(18)
5.2.3.2 Going Beyond the Paraxial Approximation: Aberrations
250(10)
5.2.3.3 Quantum Corrections to the Classical Results
260(2)
5.2.4 Normal Magnetic Quadrupole
262(5)
5.2.5 Skew Magnetic Quadrupole
267(2)
5.2.6 Axiallv Symmetric Electrostatic Lens
269(1)
5.2.7 Electrostatic Quadrupole Lens
270(1)
5.2.8 Bending Magnet
271(6)
5.3 Effect of Quantum Uncertainties on Aberrations in Electron Microscopy and Nonlinearities in Accelerator Optics
277(4)
5.4 Nonrelativistic Quantum Charged Particle Beam Optics: Spin-0 and Spinless Particles
281(2)
5.5 Appendix: Propagator for a System with Time-Dependent Quadratic Hamiltonian
283(4)
Chapter 6 Quantum Charged Particle Beam Optics: Spinor Theory for Spin-1/2 Particles
287(48)
6.1 Relativistic Quantum Charged Particle Beam Optics Based on the Dirac-Pauli Equation
287(43)
6.1.1 General Formalism
287(6)
6.1.1.1 Free Propagation: Diffraction
293(7)
6.1.1.2 Axially Symmetric Magnetic Lens
300(6)
6.1.1.3 Bending Magnet
306(10)
6.1.2 Beam Optics of the Dirac Particle with Anomalous Magnetic Moment
316(1)
6.1.2.1 General Formalism
316(4)
6.1.2.2 Lorentz and Stern-Gerlach Forces, and the Thomas-Frenkel-BMT Equation for Spin Dynamics
320(3)
6.1.2.3 Phase Space and Spin Transfer Maps for a Normal Magnetic Quadrupole
323(4)
6.1.2.4 Phase Space and Spin Transfer Maps for a Skew Magnetic Quadrupole
327(3)
6.2 Nonrelativistic Quantum Charged Particle Beam Optics: Spin-5 Particles
330(5)
Chapter 7 Concluding Remarks and Outlook on Further Developmentof Quantum Charged Particle Beam Optics
335(4)
Bibliography 339(10)
Index 349
Professor Ramaswamy Jagannathan retired in 2009 as a senior professor of physics from The Institute of Mathematical Sciences (IMSc), Chennai, India. He is currently an adjunct professor of physics at the Chennai Mathematical Institute (CMI), Chennai. He got his PhD (Theor. Phys.) from the University of Madras, Chennai, India, in 1976, working at IMSc. His PhD work on generalized Clifford algebras was done under the guidance of Professor Alladi Ramakrishnan, the founder director of IMSc known popularly as MATSCIENCE at that time. He has authored/coauthored about 80 research papers in various branches of Physical Mathematics, like Generalized Clifford Algebras and Their Physical Applications, Finite-Dimensional Quantum Mechanics, Applications of Classical Groups, Quantum Groups, Nonlinear Dynamics, Deformed Special Functions, and Quantum Theory of Charged Particle Beam Optics with Applications to Electron Microscopy and Accelerator Optics. In particular, his paper with Professors R. Simon, E. C. G. Sudarshan, and N. Mukunda (1989) on the quantum theory of magnetic electron lenses based on the Dirac equation initiated a systematic study of the Quantum Theory of Charged Particle Beam Optics. This theory was subsequently developed vastly by him and his collaborators (in particular, his PhD student Dr Sameen Ahmed Khan).

Dr Sameen Ahmed Khan is an associate professor at the Department of Mathematics and Sciences, College of Arts and Applied Sciences, Dhofar University, Salalah, Sultanate of Oman (http://du.edu.om/). He got his PhD (Theor. Phys.) at the University of Madras, Chennai, India, in 1997. His PhD thesis, done at The Institute of Mathematical Sciences (IMSc), Chennai, under the supervision of Professor Ramaswamy Jagannathan, was on the quantum theory of charged particle beam optics. He did postdoctoral research at INFN, Padova, Italy, and Universidad Nacional Autonoma de Mexico, Cuernavaca, Mexico. He has 16 years of teaching experience in Oman. He has developed a unified treatment of light beam optics and light polarization using quantum methodologies. This formalism describes the beam optics and light polarization from a parent Hamiltonian which is exact and derived from Maxwells equations. He has authored three books, fifteen book chapters, and about 75 technical publications in journals and proceedings of repute. He has more than 250 publications on science popularization. Dr Sameen is one of the founding members of the Ibn al Haytham LHiSA Light: History, Science, and Applications (LHiSA) International Society set up during the International Year of Light and Light-based Technologies. He is a signatory to six of the reports on the upcoming International Linear Collider.