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This book is intended to provide a self-contained introduction to the principles of Quantum Mechanics, based on the analysis of measurement processes of microscopic systems and the introduction of the physical observables as generators of symmetry transformations. After standard training arguments the applications are mainly focused on atomic and nuclear phenomena, as they occur on a quite different space-time scale. Thus, the text flows from the simplest systems, i.e. proton-electron in the hydrogen atom and proton-neutron in the Deuteron nucleus, to the complex many-body systems, i.e. stable states of atoms and nuclei of the periodic table, and finally to infinite many-body systems, including atomic and nuclear fluids. A digression is made on the application to astrophysical compact systems. The textbook is suitable for upper undergraduate students and graduate students in physics and related majors.
This book is a re-edition of the book "Quantum Mechanics: from Atoms to Nuclei", printed by Science Press (Beijing, 2022). Apart from the stylistic improvement of the text and the correction of a number of oversights and printing errors, this edition presents the following new subjects: (1) a brief introduction to the entangled states; the extension of the Hartree-Fock approximation to the dynamics of many body systems; (2) a review of the presentation of the nuclear giant resonances.
Umberto Lombardo (Catania, August 2024).
Preface.
Preface to the Second Edition.
Acknowledgements.
Space–Time Symmetries and Classical Observables.
Superposition Principle.
States and Dynamical Variables.
Space Translations and Momentum.
Elementary Phenomena.
Space Rotations and Angular Momentum.
Time Translations and Hamiltonian.
Harmonic Oscillations.
Approximations to the Stationary Schrödinger Equation.
Time-Dependent Equations of Motion.
Time-Dependent Perturbation Theory.
Two-Body Problem: Bound States.
Two-Body Problem: Scattering States.
Many-Body Systems.
The Dirac Equation.
Homogeneous Many-Body Systems.
Semi-classical Limit.
Collective Modes in Atomic and Nuclear Systems.
Appendix A: Vectors and Operators.
Appendix B: Special Functions in Quantum Mechanics.
Appendix C: Coupling of Angular Momenta.
Appendix D: Mathematical Complements.
Index