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Prologue Acknowledgments Author biography Glossary of symbols 1 Introduction 2 Quantum dynamics 2£®1 Hilbert vector states 2£®1£®1 iterative expansion 2£®1£®2 Basis expansion 2£®2 Subspace dynamics 2£®3 von Neumann £¨density£© matrix states 2£®3£®1 IP iterative expansion 2£®4 Homework problems References 3 Atomic potentials 3£®1 Central field 3£®2 Harmonic oscillator 3£®3 Homework problems References 4 Laser pulses 4£®1 Classical electrodynamics 4£®2 Laser pulses in the paraxial approximation 4£®3 Coherent and partially coherent fields 4£®4 Homework problems References 5 Quantum systems in laser fields 5£®1 Atomic TDSE in the dipole approximation 5£®2 Time-dependent perturbation theory 5£®3 Driven quantum oscillator 5£®4 Homework problems References 6 Amplitude coefficient equations 6£®1 Two-level systems 6£®2 Ionization 6£®2£®1 Single-photon ionization 6£®3 Resonant excitation and £¨auto-£©ionization 6£®4 Homework problems References 7 Density-matrix element equations 7£®1 Resonant ionization 7£®2 Ionization in stochastic fields 7£®2£®1 Averaged equations for resonant auto-ionization 7£®3 Homework problems References ¡­¡­ 8 Matrix elements of atomic operators 9 TDSE of hydrogen-like atoms in laser fields 10 Space division of a one-dimensional TDSE 11 Quantum mechanics of vector- and matrix-states 12 Technicalities Appendix A£º Mathematical formalism ±à¼­ÊÖ¼Ç