QUANTUM PHYSICS II
Quantum mechanics I. Principles of analytical mechanics and electromagnetism. We will also use mathematical tools introduced in the course of mathematical methods for physics.
The exam is divided into two parts:
-a written test (3 hours) consisting in two to three exercises (30 points in total) covering the main topics studied in the course, which will test the ability of students in applying the techniques learned in class to problems of nonrelativistic quantum mechanics;
- an oral part, where the understanding of the quantum mechanics basic tools introduced during the course will be assessed, evaluating the acquisition of the technical skills and the rigor of presentation. To pass the exam, it will be necessary to satisfactorily present 1 or 2 of the topics studied during the course, describing their main characteristics. Access to the oral exam requires a mark of at least 16/30 at the written part.
Each part will be evaluated with a grade in the range 0 to 30, and the final grade will be the average, if greater than or equal to 18, of the grades of the two parts. Full marks with laude are assigned only to students who demonstrate thorough knowledge and understanding of all the course topics and excellent presentation skills.
This course is designed to complement the student's knowledge in the field of non-relativistic quantum mechanics, applied to the case of a single particle in force fields. Both exactly solvable problems and approximate methods will be addressed, in order to complete the technical background for the application of quantum mechanics to the basic problems of modern physics.
Expected Learning Outcomes.
Upon completion of the Course, students will be able to:
1) Describe the main tools of quantum mechanics for the study of single-particle systems in force fields;
2) Solve basic quantum mechanical exercises in more than one dimension and apply approximate methods to the same problems;
3) Discuss the basic tools used for quantum mechanics in more than one dimension.
General theory of angular momentum;
exactly solvable systems; approximate methods.
Detailed course program:
1) General theory of angular momentum: orbital angular momentum in quantum mechanics, spherical harmonics, the relationship between the rotations of a system in three-dimensional space and the rotation operators applied to a state in the Hilbert space of the system, rotations for many-particle systems, spin angular momentum, the Pauli spinors, addition of two angular momenta, Clebsch-Gordan coefficients, Wigner-Eckart theorem.
2) Exactly solvable systems: rotator, quasi-classical states of a rotator, two-dimensional harmonic oscillator, coherent states of a two-dimensional oscillator, charged particle in a uniform magnetic field and Landau levels, motion in a central potential, free motion in three dimensions, three-dimensional harmonic oscillator, Coulomb potential and hydrogen atom.
3) Approximate methods: scattering processes (partial waves analysis, phase shifts, the Born approximation), time-independent perturbations (nondegenerate perturbation theory, the Rayleigh-Schrödinger expansion, degenerate perturbation theory, applications: the Stark effect, two-level systems), the WKB method, the adiabatic approximation and Berry’s phase.
In-person lectures during which the theoretical concepts of the course will be introduced and exercises solved.
Office hours for students: by appointment, office V4.7 fourth floor, via Valleggio 11 (lucia.caspani@uninsubria.it).