Quantum Mechanics 1100-3001
The course aims to introduce students to the fascinating world of microscopic objects described by the laws of non-relativistic quantum mechanics. Attention will be focused on building participants' "quantum intuition" through applications of the theory to description of phenomena in the world of atoms, molecules, and nuclei.
Program:
1. Wave function and the Schrödinger equation. Linearity of the Schrödinger equation and its consequences.
2. Postulates of quantum mechanics. Quantum observables. Uncertainty principle.
3. Classification of solutions to the Schrödinger equation: states of a free particle, states of a particle bound in a potential well, scattering states, band-like solutions in periodic systems.
4. Harmonic oscillator. Creation and annihilation operators.
5. Quantum theory of angular momentum. Spin. Quantum-mechanical coupling of angular momenta.
6. Particle in a spherically symmetric potential. Hydrogen atom.
7. Motion of a charged particle in the electromagnetic field.
8. Methods of approximate solution to the Schrödinger equation : stationary perturbation theory, variational method, WKB approximation.
9. Time-dependent perturbation theory. Ionization of the Hydrogen atom. The Fermi golden-rule.
10. Quantum theory of scattering: the Born series and partial waves.
11. Elements of quantum many-body theory: molecular orbitals and molecular binding in H2 molecule, the Fermi-gas model, mean-field approximation.
12. Quantum nature of the Standard Model and its secrets.
Courses required before attending:
Mathematical Analysis, Algebra with Geometry, or Mathematics, Physics IV, Classical Mechanics
Completion rules:
Completion of classes and passing exam - details of credits allocation will be announced at the course beginning.
Time estimates:
Lecture = 60 hours
Classes = 60 hours
Homework problems = 70 hours
Preparation for tests and exams = 70 hours
Total of about 260 hours
Description composed by Stanisław Głazek, July 2013.
Mode
Prerequisites (description)
Learning outcomes
Knowledge:
- knowledge of physical effects demonstrating incompatibility of classical physics with microscopic world
- mastering basic notions and mathematical formalism of quantum mechanics
- comprehension of the quantum picture of physical quantities, such as energy, angular momentum, etc.
Skills:
- solving standard problems in nonrelativistic quantum mechanics
- describing quantum phenomena using simple mathematical models
- explaining effects resulting from wave-particle duality and quantum interference
Assessment criteria
- homework
- tests
- final written exam
- final oral exam
Practical placement
none
Bibliography
1. L. Schiff, Quantum Mechanics.
2. L.D. Landau and E.M. Lifszyc, Quantum Mechanics.
3. I. Białynicki-Birula, M. Cieplak, and J. Kamiński, Theory of Quanta.
4. B.G. Englert, Lectures on Quantum Mechanics.
5. R.L. Liboff, Introductory Quantum Mechanics.
6. R. Shankar, Mechanika kwantowa.
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:
Additional information (registration calendar, class conductors, localization and schedules of classes), might be available in the USOSweb system: