This textbook is addressed to graduate and post-graduate students in Physics.lt 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.

Chapter 1 Space-Time Symmetries and Classical Observables
1.1 Hamilton's Equations
1.2 Space-Time Symmetries and Conservation of Dynamical Variables
1.3 Canonical Transformations and Space-Time Symmetries
1.4 Notes and References
1.5 Problems
Chapter 2 Superposition Principle
2.1 An Historic Experiment
2.2 Wave-like Behaviour of Particles
2.3 Particle-like Behaviour of Waves
2.4 The Stern-Gerlach Experiment
2.5 Notes and References
2.6 Problems
Chapter 3 States and Dynamical Variables
3.1 States of a Quantum System as Vectors of Hilbert Space ..,
3.2 Observables as Operators in Hilbert Space
3.3 General Properties of Quantum Observables
3.4 Unitary Transformations
3.5 Notes and References
3.6 Problems
Chapter 4 Space Translations and Momentum
4.1 Wave Function and Position Operator
4.2 Space Translations
4.3 Momentum as a Generator of Infinitesimal Translations ...
4.4 Free Particle in a Box
4.5 Heisenberg Uncertainty Relations
4.6 Notes and References
4.7 Problems
Chapter 5 Elementary Phenomena
5.1 Double-Slit Interference
5.2 Diffraction Grating
5.3 Double-Layer Reflection
5.4 Scattering of Identical Particles
5.5 Notes and References
5.6 Problems
Chapter 6 Space Rotations and Angular Momentum
6.1 Space Rotations
6.2 Orbital Angular Momentum as Generator of Infinitesimal Rotations
6.3 Properties of the Angular Momentum
6.4 Orbital Angular Momentum in Polar Coordinates
6.5 Reflection of Axes and Parity
6.6 Spin
6.7 The Rigid Rotor
6.8 Complement to Sec.6.1 : Infinitesimal Space Rotations
6.9 Notes and References
6.10 Problems
Chapter 7 Time Translations and Hamiltonian
7.1 Time Evolution Operator
7.2 Equations of Motion
7.3 Stationary SchrSdinger Equation
7.3.1 SchrSdinger Equation for Potential Wells
7.3.2 Attractive Well: Vo < 0
7.3.3 Repulsive Well: V0 > 0
7.3.4 Potential Barrier: 0 < E < V0
7.3.5 Potential Barrier: E > V0 > 0
7.4 Problems
Chapter 8 Harmonic Oscillations
8.1 Quantum Harmonic Oscillator
8.1.1 Eigenfunctions of the Harmonic Oscillator
8.2 Vibrations of a Crystal Lattice
8.2.1 Small Oscillations in Classical Approach
8.2.2 Small Oscillations in Quantum Approach
8.3 Three-Dimensional Harmonic Oscillator
8.4 Notes and References
8.5 Problems
Chapter 9 Approximations to Schr~idinger's Equation
9.1 Perturbation Theory
9.1.1 Non-Degenerate Case
9.1.2 Degenerate Case
9.2 Variational Approach
9.3 Perturbation vs. Variational Approximations for 4He
9.3.1 Perturbation Method
9.3.2 Variational Estimate
9.4 Problems
Chapter 10 Time-Dependent Equations of Motion
10.1 Heisenberg Representation
10.2 Two-Level Quantum System
10.2.1 Unperturbed Hamiltonian
10.2.2 Perturbation Potential
10.2.3 Time-Dependent Hamiltonian
10.3 Relationship between Symmetries and Conservation Theorems
10.4 Classical Limit: Ehrenfest Theorem
10.5 Particle Detection in Scattering Processes
10.6 Problems
Chapter 11 Time-Dependent Perturbation Theory
11.1 Interaction Representation
11.2 Electron Transitions in Atoms
11.3 Dipole Approximation
11.4 Slow vs. Fast Processes
11.5 Complement to Sec.11.2: Interaction of Charged Particles with the Electromagnetic Field
11.6 Notes and References
11.7 Problems
Chapter 12 Two-Body Problem: Bound States
12.1 Central Potential
12.2 Hydrogen Atom
12.3 Isospin
12.4 Ground State of the Deuteron
12.5 Complement to Sec.12.4: Tensor Interaction
12.6 Notes and References
12.7 Problems
Chapter 13 Two-Body Problem: Scattering States
13.1 Lippmann-Schwinger Equation
13.2 Asymptotic Form of the Continuum States
13.3 Solving the Lippmann-Schwinger Equation
13.4 Elastic Scattering Cross Section
13.4