**Description:**

The
dynamics of quantum systems exposed to ultrafast (at the femtosecond
time-scale) and strong laser radiation has a highly non-linear character,
leading to a number of new phenomena, outside the reach of traditional
spectroscopy. The current laser technology makes feasible the probing and
control of quantum-scale systems with fields that are as strong as the
interatomic Coulombic interactions and time resolution that is equal to (or
less than) typical atomic evolution times. It is indispensable that any
theoretical description of the induced physical processes should rely on the
accurate calculation of the atomic structure and a realistic model of the laser
radiation as pulsed fields. This book aims to provide an elementary
introduction of theoretical and computational methods and by no means is
anywhere near to complete. The selection of the topics as well as the
particular viewpoint is best suited for early-stage students and researchers;
the included material belongs in the mainstream of theoretical approaches
albeit using simpler language without sacrificing mathematical accuracy.
Therefore, subjects such as the Hilbert vector-state, density-matrix operators,
amplitude equations, Liouville equation, coherent laser radiation,
free-electron laser, Dyson-chronological operator, subspace projection, perturbation theory,
stochastic density-matrix equations, time-dependent Schroedinger equation,
partial-wave analysis, spherical-harmonics expansions, basis and grid
wavefunction expansions, ionization, electron kinetic-energy and angular
distributions are presented within the context of laser-atom quantum dynamics.

Contents:

**Prologue**

**Acknowledgments**

** Author biography**

**Glossary of symbols **

**Chapter 1.
Introduction**

**Chapter 2. Quantum
dynamics** • Hilbert vector states • Iterative expansion • Basis
expansion • Subspace dynamics • von Neumann (density) matrix states • IP
iterative expansion Homework problems • References

**Chapter 3. Atomic
potentials** • Central field • Harmonic oscillator • Homework
problems • References

**Chapter 4. Laser
pulses **• Classical electrodynamics • Laser pulses in the
paraxial approximation • Coherent and partially coherent fields • Homework
problems • References

**Chapter 5. Quantum
systems in laser fields **• Atomic TDSE in the dipole
approximation • Time-dependent perturbation theory • Elements of
Photoionization Quantum Dynamics Methods • Driven quantum oscillator • Homework
problems • References

**Chapter 6. Amplitude
coefficient equations** • Two-level systems • Ionization •
Single-photon ionization • Resonant excitation and (auto-)ionization • Homework
problems • References

**Chapter 7. Density-matrix
element equations** • Resonant ionization • Ionization in
stochastic fields • Averaged equations for resonant auto-ionization • Homework
problems • References

**Chapter 8. Matrix
elements of atomic operators** • Atomic operators on the angular basis
• Central-field Hamiltonian and dipole operators • Molecular diatomic potential
• Inversion symmetry (parity) • Plane waves as a momentum basis • One- and
two-electron ionization amplitudes • Homework problems • References

**Chapter 9. TDSE of
hydrogen-like atoms in laser fields** • Spectral and angular
basis formulation • Spectral basis • Angular basis • Calculation of observables
• Practical considerations • Homework problems • References

**Chapter 10. Space
division of a one-dimensional TDSE** • Time-independent potential
• Time-dependent potential • Homework problems • References

**Chapter 11. Quantum
mechanics of vector- and matrix-states** • Vectors and operators •
Statistical matrix state (or density matrix) • Density-state operator •
Position representation • Degenerate systems • Homework problems • References

**Chapter 12.
Technicalities** • Radial atomic Schrödinger equation •
Calculation of radial eigenstates • Box-normalization of the continuum states •
Free boundary conditions • Time-propagation methods • *B*-spline
polynomial basis • References

**Appendix A:
Mathematical formalism **

About the Author:

**Lampros Nikolopoulos, **PhD, is a lecturer at
the School of Physical Sciences at Dublin City University (DCU). He was brought
up in Greece and holds a BSc (Hons) in physics from the Physics Department of
the University of Athens, and an MSc and PhD in theoretical atomic physics from
the University of Crete, Greece. His previous posts include MPQ-Garching in
Germany, IFA-Aarhus in Denmark, and QUB-Belfast in the UK, before he settled in
Dublin. His research interests include ultra-short laser-matter quantum
dynamics and development of high-performance computational methods. A recent
thesis supervised by him received a prize from the UK-IOP Computational Group
as the ‘Best PhD Thesis in Compuational Physics’ for the year 2016. He has
(co)authored over 80 journal articles, two book chapters and co-edited a
special issue on ‘*short-wavelength free electron lasers*’.

Target Audience:

This
book is intended for new comers who would like to have an introductory (soft)
crash- course in ultra- short laser- atomic dynamics methods. It is useful for
people interested in quantum mechanics and physics.