Preface |
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xi | |
Authors |
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xv | |
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1 | (8) |
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Chapter 2 An Introductory Review of Classical Mechanics |
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9 | (32) |
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2.1 Single Particle Dynamics |
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9 | (32) |
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2.1.1 Lagrangian Formalism |
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9 | (1) |
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9 | (1) |
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2.1.1.2 Example: Motion of a Charged Particle in an Electromagnetic Field |
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10 | (2) |
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2.1.2 Hamiltonian Formalism |
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12 | (1) |
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12 | (2) |
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2.1.2.2 Example: Motion of a Charged Particle in an Electromagnetic Field |
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14 | (2) |
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2.1.3 Hamiltonian Formalism in Terms of the Poisson Brackets |
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16 | (1) |
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16 | (2) |
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2.1.3.2 Example: Dynamics of a Charged Particle in a Constant Magnetic Field |
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18 | (3) |
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2.1.4 Changing the Independent Variable |
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21 | (1) |
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21 | (1) |
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2.1.4.2 Example: Dynamics of a Charged Particle in a Constant Magnetic Field |
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22 | (3) |
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2.1.5 Canonical Transformations |
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25 | (1) |
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25 | (4) |
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2.1.5.2 Optical Hamiltonian of a Charged Particle Moving Through an Electromagnetic Optical Element with a Straight Axis |
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29 | (2) |
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2.1.6 Symplecticity of Canonical Transformations |
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31 | (1) |
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2.1.6.1 Time-Independent Canonical Transformations |
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31 | (1) |
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2.1.6.2 Time-Dependent Canonical Transformations: Hamiltonian Evolution |
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32 | (3) |
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2.1.6.3 Canonical Invariants: Poisson Brackets |
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35 | (1) |
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2.2 Dynamics of a System of Particles |
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36 | (5) |
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Chapter 3 An Introductory Review of Quantum Mechanics |
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41 | (132) |
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41 | (1) |
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3.2 General Formalism of Quantum Mechanics |
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42 | (36) |
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3.2.1 Single Particle Quantum Mechanics: Foundational Principles |
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42 | (1) |
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3.2.1.1 Quantum Kinematics |
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42 | (9) |
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51 | (13) |
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3.2.1.3 Different Pictures of Quantum Dynamics |
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64 | (4) |
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3.2.1.4 Ehrenfest's Theorem |
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68 | (2) |
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70 | (8) |
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3.3 Nonrelativistic Quantum Mechanics |
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78 | (54) |
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3.3.1 Nonrelativistic Single Particle Quantum Mechanics |
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78 | (1) |
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78 | (12) |
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3.3.1.2 Linear Harmonic Oscillator |
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90 | (10) |
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3.3.1.3 Two-Dimensional Isotropic Harmonic Oscillator |
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100 | (3) |
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3.3.1.4 Charged Particle in a Constant Magnetic Field |
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103 | (4) |
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3.3.1.5 Scattering States |
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107 | (4) |
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3.3.1.6 Approximation Methods, Time-Dependent Systems, and the Interaction Picture |
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111 | (6) |
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3.3.1.7 Schrodinger-Pauli Equation for the Electron |
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117 | (2) |
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3.3.2 Quantum Mechanics of a System of Identical Particles |
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119 | (7) |
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3.3.3 Pure and Mixed States: Density Operator |
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126 | (6) |
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3.4 Relativistic Quantum Mechanics |
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132 | (38) |
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3.4.1 Klein-Gordon Equation |
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132 | (1) |
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3.4.1.1 Free-Particle Equation and Difficulties in Interpretation |
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132 | (5) |
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3.4.1.2 Feshbach-Villars Representation |
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137 | (2) |
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3.4.1.3 Charged Klein-Gordon Particle in a Constant Magnetic Field |
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139 | (2) |
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141 | (1) |
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3.4.2.1 Free-Particle Equation |
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141 | (8) |
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149 | (1) |
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3.4.2.3 Spin and Helicity of the Dirac Particle |
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150 | (3) |
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3.4.2.4 Spin Magnetic Moment of the Electron and the Dirac-Pauli Equation |
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153 | (1) |
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3.4.2.5 Electron in a Constant Magnetic Field |
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154 | (2) |
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3.4.3 Foldy-Wouthuysen Transformation |
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156 | (1) |
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3.4.3.1 Foldy-Wouthuysen Representation of the Dirac Equation |
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156 | (12) |
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3.4.3.2 Foldy-Wouthuysen Representation of the Feshbach-Villars form of the Klein-Gordon Equation |
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168 | (2) |
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3.5 Appendix: The Magnus Formula for the Exponential Solution of a Linear Differential Equation |
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170 | (3) |
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Chapter 4 An Introduction to Classical Charged Particle Beam Optics |
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173 | (40) |
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4.1 Introduction: Relativistic Classical Charged Particle Beam Optics |
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173 | (1) |
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174 | (4) |
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4.3 Optical Elements with Straight Optic Axis |
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178 | (28) |
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4.3.1 Axially Symmetric Magnetic Lens: Imaging in Electron Microscopy |
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178 | (19) |
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4.3.2 Normal Magnetic Quadrupole |
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197 | (5) |
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4.3.3 Skew Magnetic Quadrupole |
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202 | (2) |
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4.3.4 Axially Symmetric Electrostatic Lens |
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204 | (1) |
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4.3.5 Electrostatic Quadrupole |
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205 | (1) |
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4.4 Bending Magnet: An Optical Element with a Curved Optic Axis |
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206 | (4) |
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4.5 Nonrelativistic Classical Charged Particle Beam Optics |
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210 | (3) |
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Chapter 5 Quantum Charged Particle Beam Optics: Scalar Theory for Spin-0 and Spinless Particles |
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213 | (74) |
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5.1 General Formalism of Quantum Charged Particle Beam Optics |
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213 | (1) |
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5.2 Relativistic Quantum Charged Particle Beam Optics Based on the Klein-Gordon Equation |
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214 | (63) |
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214 | (16) |
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5.2.2 Free Propagation: Diffraction |
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230 | (2) |
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5.2.3 Axially Symmetric Magnetic Lens: Electron Optical Imaging |
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232 | (1) |
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5.2.3.1 Paraxial Approximation: Point-to-Point Imaging |
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232 | (18) |
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5.2.3.2 Going Beyond the Paraxial Approximation: Aberrations |
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250 | (10) |
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5.2.3.3 Quantum Corrections to the Classical Results |
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260 | (2) |
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5.2.4 Normal Magnetic Quadrupole |
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262 | (5) |
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5.2.5 Skew Magnetic Quadrupole |
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267 | (2) |
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5.2.6 Axiallv Symmetric Electrostatic Lens |
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269 | (1) |
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5.2.7 Electrostatic Quadrupole Lens |
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270 | (1) |
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271 | (6) |
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5.3 Effect of Quantum Uncertainties on Aberrations in Electron Microscopy and Nonlinearities in Accelerator Optics |
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277 | (4) |
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5.4 Nonrelativistic Quantum Charged Particle Beam Optics: Spin-0 and Spinless Particles |
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281 | (2) |
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5.5 Appendix: Propagator for a System with Time-Dependent Quadratic Hamiltonian |
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283 | (4) |
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Chapter 6 Quantum Charged Particle Beam Optics: Spinor Theory for Spin-1/2 Particles |
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287 | (48) |
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6.1 Relativistic Quantum Charged Particle Beam Optics Based on the Dirac-Pauli Equation |
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287 | (43) |
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287 | (6) |
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6.1.1.1 Free Propagation: Diffraction |
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293 | (7) |
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6.1.1.2 Axially Symmetric Magnetic Lens |
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300 | (6) |
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306 | (10) |
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6.1.2 Beam Optics of the Dirac Particle with Anomalous Magnetic Moment |
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316 | (1) |
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6.1.2.1 General Formalism |
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316 | (4) |
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6.1.2.2 Lorentz and Stern-Gerlach Forces, and the Thomas-Frenkel-BMT Equation for Spin Dynamics |
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320 | (3) |
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6.1.2.3 Phase Space and Spin Transfer Maps for a Normal Magnetic Quadrupole |
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323 | (4) |
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6.1.2.4 Phase Space and Spin Transfer Maps for a Skew Magnetic Quadrupole |
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327 | (3) |
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6.2 Nonrelativistic Quantum Charged Particle Beam Optics: Spin-5 Particles |
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330 | (5) |
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Chapter 7 Concluding Remarks and Outlook on Further Developmentof Quantum Charged Particle Beam Optics |
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335 | (4) |
Bibliography |
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339 | (10) |
Index |
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349 | |