Computing Atomic Quantum Dynamics in Laser Fields

Computing Atomic Quantum Dynamics in Laser Fields introduces theory in tandem with practical methods to calculate end numbers-teaching typically separate subjects together. The topics covered are at the core of several contemporary areas of theoretical atomic, molecular, and optical physics (AMO) including ultrashort laser fields, quantum dynamics and control, quantum imaging, and computational physics. High performance algorithms, numerical analysis, and differential and matrix calculus are presented in the context of the theory of laser atom dynamics. Computing Atomic Quantum Dynamics in Laser Fields: -- Combines practical numerical methods in computing atomic processes in ultrashort laser fields in a systematic and coherent manner -- Shortens learning time for mastering computational techniques in atomic, molecular, and optical research -- Presents theoretical formulations in a manner that fits naturally with the discrete nature of computational algorithms Post-graduate students and practitioners in the field of AMO and computational physics will find this an invaluable resource. Cover Half Title Title Page Copyright Page Preface Table of Contents Chapter 1: Introduction to Atom–Laser Dynamics 1.1 TDSE OF ATOMS IN LASER FIELDS 1.2 TDSE IN THE ENERGY BASIS 1.3 FIRSTAND SECOND-ORDER APPROXIMATIONS 1.4 ac-STARK SHIFT AND IONIZATION WIDTH 1.5 BASICS OF TIME-DEPENDENT PERTURBATION THEORY REFERENCES Chapter 2: Basics of Differential and Matrix Calculus 2.1 LINEAR ODEs AND ORTHOGONAL FUNCTIONS 2.2 A MINIMUM ON MATRICES 2.3 TRIDIAGONAL MATRICES 2.4 PROBLEMS REFERENCES Chapter 3: Spatial Approximation 3.1 FROM DIFFERENTIAL TO MATRIX CALCULUS 3.2 FINITE DIFFERENCES (FD) METHOD 3.3 IMPLEMENTING THE BOUNDARY CONDITIONS 3.4 SOME PRACTICALITIES PROBLEMS REFERENCES Chapter 4: Time Approximation 4.1 INITIAL-VALUE ODEs ON A (x, t ) LATTICE 4.2 EXPONENTIATION APPROXIMATION METHODS 4.3 LANCZOS SUBSPACE DYNAMICS 4.4 PROBLEMS REFERENCES Chapter 5: Laser Pulses 5.1 CLASSICAL ELECTRODYNAMICS 5.2 PULSE MODELING REFERENCES Chapter 6: TDSE as a Space–Time Differential Equation 6.1 THE FIELD-FREE TDSE 6.2 FREE RADIAL MOTION 6.3 BOX EIGENSTATES AS LOCALIZED WAVEPACKETS AND R-MATRIX 6.4 RADIAL FUNCTIONS OF A GENERAL ATOMIC POTENTIAL 6.5 PROBLEMS REFERENCES Chapter 7: Atomic Structure of Hydrogenic Systems 7.1 CENTRAL-FIELD ONE-ELECTRON HAMILTONIAN 7.2 SPHERICAL HARMONICS, THE ANGULAR BASIS 7.3 RADIAL EIGENSTATES ON A B-SPLINE BASIS 7.4 FINITE ELEMENTS: ELASTIC BCs 7.5 WKB NORMALIZATION OF UNBOUND STATES REFERENCES Chapter 8: TDSE of Hydrogen 8.1 INTERACTION OF AN ELECTROMAGNETIC FIELD WITH ELECTRONS 8.2 RADIAL TDSE 8.3 GRID AND BASIS TDSE SOLUTIONS 8.4 PRACTICAL CONSIDERATIONS REFERENCES Chapter 9: Ionization Dynamics of Wavepackets 9.1 INTRODUCTION 9.2 FIRST-ORDER THEORY OF THE WAVEPACKET 9.3 THE ASYMPTOTIC MOMENTUM BASIS 9.4 ONE-PHOTON HYDROGEN CROSS SECTION 9.5 CONCLUDING REMARKS 9.6 APPENDIX: FAR-REGION RADIAL WAVEPACKETS REFERENCES Chapter 10: Hydrogen Ionization 10.1 OBSERVABLES AND PROJECTION APPROACH 10.2 CALCULATION OF EXCITATION/IONIZATION OBSERVABLES 10.3 POPULATION/IONIZATION USING FD FUNCTIONS REFERENCES Index