|SCIENTIFIC DISCIPLINARY SECTOR||FIS/02|
You can take the exam for this unit if you passed the following exam(s):
The course discusses the main experimental evidences that motivate abandoning classical mechanics to describe atomic physics. The fundamental principles of non-relativistic quantum mechanics and its mathematical formalism are presented. Applications of quantum mechanics to the physics of particles, atoms, molecules, gases and condensed matter are described. In the second part of the course approximation methods and scattering theory are developed.
At the end of this lecture course, the student will have developed a good understanding of quantum mechanics basic principles, as well as the theory's mathematical foundations. The student will be able to apply this knowledge to solve concrete problems involving physical phenomena at the atomic scale, both exactly and by using approximation methods
At the end of these courses the student will be able to
Basic knowledge of classical mechanics and analytical mechanics, mathematical analysis, geometry and linear algebra.
The course is delivered through frontal lectures that include
A1 The crisis of classical physics
1.1 Atomic models
1.2 Photoelectric effect and photons
1.3 Compton effect
1.4 Atomic absorption and emission spectra
A2 The old quantum theory
2.1 Bohr atomic model
2.2 De Broglie wavelength and wave-particle duality
2.3 Bohr-Sommerfeld quantization rule
2.4 Davisson e Germer experiment
2.7 Particle interference
A3 The formalism of quantum mechanics
3.1 Superposition principle: states and vectors
3.2 Scalar products and transition probabilities
3.3 Observables, operators and eigenvector basis
3.4 Compatible and incompatible observables
3.5 Equivalent representations and unitary transformations
3.6 Quantum systems with finite basis
A4 Particle Quantum mechanics
4.1 Uncertainty relations
4.2 Canonical relations
4.3 Continuous spectrum: generalized eigenstates and observables
4.4 Coordinates and momenta representations
4.5 Wave packets
4.6 Schrödinger equation
A5 Temporal evolution
5.1 Schrödinger and Heisenberg pictures
5.2 Time evolution of a Gaussian packet
5.3 Continuity equation
5.4 Collective interpretation of the wave function
A6 One-dimensional Schrödinger equation
6.1 Free particle
6.2 Particle in a box
6.3 General properties of energy eigenfunctions in 1 dimension
6.4 Step potential
6.5 Square potential well
6.6 Potential barrier: transmission and reflection coefficients
6.7 Tunnel effect: semi-classical limit. Alpha decay
6.8 Harmonic oscillator: creation and destruction operators
7.1 Translations and rotations
7.2 Discrete translations: Bloch theorem
7.3 Angular momentum and its representations
7.5 Addition of angular momenta
7.6 Scalar and vector operators
7.7 Harmonic polynomials and spherical harmonics
7.8 Schrödinger equation in central potential
7.9 The levels and the energy eigenfunctions of the hydrogenoides
A8 Atoms and Molecules
8.1 Fundamental level of Helium
8.2 Excited levels of Helium
8.3 Identical particles: bosons and fermions
8.4 Pauli principle
8.5 Zeeman effect
B.I: Advanced topics in QM (3 weeks)
1. Symmetries in Quantum Mechanics
2. Selection rules for scalar and vector operator. Wigner-Eckhart theorem.
3. Mixed-states, density matrix
B.II: Approximation methods (4 weeks)
1. Time-independent perturbation theory: degenerate and non-degenerate case.
2. Applications to hydrogenoids: fine and hyperfine structure, Zeeman effect.
3. Variational methods
4. WKB approximation
B.III: Time-dependent Hamiltonians and Scattering (4 weeks)
1. Formal solution of the Schrodinger equation with time-dependent hamiltonians. Dyson series. Exact solutions: spin resonance.
2. Time-dependent perturbation theory. Interactions with classical radiation. The adiabatic approximation.
3. Elastic scattering: time-dependent and time-independent formalism. Lippmann Schwinger equation. Born approximation.
4. Partial waves expansion.
B.IV: Towards Relativistic Quantum Mechanics (1 week)
1. Klein-Gordon and Dirac equation.
Office hours: Please schedule an appointment by e-mail.
Office hours: Please schedule an appointment, in person or on Teams, by e-mail. Camillo Imbimbo, Dipartimento di Fisica, Via Dodecaneso 33, 16146 Genova Office 717, Floor 7, phone: 0103536449 firstname.lastname@example.org
CAMILLO IMBIMBO (President)
All class schedules are posted on the EasyAcademy portal.
The exam is made up a written test and an oral part. Rules and criteria and specified on the course aulaweb page.
The written test has a duration of 4 hours and contains two problems, one for each part of the course. The problems are divided into questions of variable difficulty, in order to more accurately evaluate the level of competence achieved by the student.
The oral exam, which lasts about 40 minutes, is lead by two professors responsible for the two parts of the course. During the oral exam the student is asked to answer a few questions or to solve problems at the blackboard, in order to assess the student’s knowledge and understanding of the topic discussed. During the lectures, students will be given the opportunity to solve problems and exercises, as a means of self-evaluation.