Quantum mechanics 1100-2Ind11
The aim of this lecture is to present a quantum description of the behavior of a single particle and simple atomic systems.
1. The wave function and the Schrödinger equation. The linearity of the Schrödinger equation and its consequences. Ehrenfest's theorem and the classical correspondence principle.
2. Postulates of quantum mechanics. The Hilbert space of quantum states of a system. Quantum observables. The uncertainty principle. Time evolution of a system. Elements of measurement theory.
3. Classification of solutions to the Schrödinger equation: states of a free particle, states of a particle bound in a potential well, scattering states, and band solutions in periodic systems.
4. The harmonic oscillator. Creation and annihilation operators. Coherent states. Algebraic methods in quantum mechanics.
5. Quantum theory of angular momentum. Spin. Elements of the theory of angular momentum composition.
6. Motion in a central force field. The hydrogen atom.
7. Motion of a charged particle in an electromagnetic field. Berry's geometric phases and the Aharonov-Bohm effect.
8. Approximate methods for solving the Schrödinger equation: stationary perturbation theory, variational method, WKB approximation.
9. Time-dependent perturbation theory. Ionization of the hydrogen atom. The photoelectric effect. Fermi's golden rule.
10. Quantum scattering theory: Born series and partial wave method. Lippmann-Schwinger equation.
11. Description of a mixed-state system. Density operator. Measurement theory on mixed-state systems. Elements of decoherence theory.
12. The Dirac equation for relativistic particles. Elementary properties and solutions. Relativistic corrections to the Schrödinger equation.
Required pre-lecture coursework:
Mathematical Analysis and Algebra with Geometry or Mathematics, Physics III, Classical Mechanics
Course coordinators
Term 2025L: | Term 2024L: |
Mode
Prerequisites (description)
Learning outcomes
Wiedza:
- znajomość zjawisk kwantowych na poziomie mikroskopowym
- opanowanie podstawowych pojęć i formalizmu matematycznego mechaniki kwantowej, w tym struktury przestrzeni Hilberta i operatorów kwantowych do wyjaśniania zjawisk fizycznych na poziomie mikroskopowym
Umiejętności:
- rozwiązywanie standardowych zagadnień nierelatywistycznej mechaniki kwantowej
- opis zjawisk kwantowych za pomocą prostych modeli matematycznych
- wyjaśnianie efektów wynikających z dualizmu korpuskularno-falowego i interferencji kwantowej
Assessment criteria
Midterm exam (30 points)
Final exam (40 points)
Weekly homework (30 points)
Total 100 points (initial suggested grades: 50-60 = 3, 60-70 = 3.5, 70-80 = 4, 80-90 = 4.5, 90-100 = 5).
Oral exam for students with a grade >3 (grade change of no more than 0.5)
Practical placement
none
Additional information
Information on level of this course, year of study and semester when the course unit is delivered, types and amount of class hours - can be found in course structure diagrams of apropriate study programmes. This course is related to the following study programmes: