Quantum Mechanics I (in English) 1102-301A

The intent of this course is to introduce students to intriguing phenomena and processes occurring in the microscopic world, which is described by quantum mechanics. During the lecture, students will get to know the foundations of non-relativistic quantum mechanics in relation to numerous experimental facts, which had an influence on how the theory has developed. The emphasis will be on applications of theory of quanta in relation to specific physical problems, which are basic for our current understanding of the world of micro-objects such as atoms, molecules or nuclei. The role of symmetries in quantum mechanics and their relation to conservation laws will be stressed. During the recitations, students will develop practical abilities using the concepts, mathematical methods, and the laws of quantum mechanics. Various pedagogical techniques will be used such as interactive engagement and peer instruction, to ensure a more complete understanding.

Program:
1. Postulates of quantum mechanics.
2. Pure and mixed states.
3. The Born postulates, quantum observables. Quantum dynamics.
4. Entangled states. Entropy and information. Qubit.
4. The Schrödinger equation.
5. Position and momentum of a quantum particle: principle of uncertainty.
6. Quantum phase space. The Wigner function.
7. Classification of solutions to the Schrödinger equation.
9. Bound states and energy levels.
10. Charged particle in electromagnetic field.
11. Spin of a quantum particle and the Pauli equation.
12. Harmonic oscillator.
13. Quantum theory of angular momentum.
14. Particle in a spherically symmetric potential. Hydrogen atom.
15. Approximate methods in quantum mechanics.
16. Perturbation theory for bound states, the WKB method, time-dependent perturbation theory.
17. The golden Fermi rule. Emission and absorption of radiation.
18. Quantum theory of scattering. The Born approximation, partial waves.

Expected student workload:
lecture – 60h
recitations – 60h
homeworks – 45h
preparations to mid-term exams – 60h
preparations to exams – 45h
Total – 270h

Description by Stanisław D. Głazek (June 2007), updated by Katarzyna Krajewska (May 2010).

Main fields of studies for MISMaP

physics

Mode

Classroom

Prerequisites (description)

The course is aimed at students who have passed the courses on Calculus and Algebra (or, equivalent courses on Mathematics), and who know Classical mechanics. Also, it is advised to the students to pass courses: Physics IV or Foundations of quantum physics and matter structure. Students must know English; however they do not have to know the specialized terms used in quantum mechanics, as they will learn them during the course.

Course coordinators

Kazuki Sakurai
Wojciech Satuła

Learning outcomes

Student:
1. knows basic concepts of quantum mechanics
2. applies these concepts in description of quantum phenomena
3. knows and uses necessary mathematical methods
4. uses both wave- and matrix formulations
5. solves the Schrödinger equation
6. knows and uses approximate methods
7. describes relations between classical and quantum mechanics
8. uses Polish and English terminology

Assessment criteria

Assessment form: passing the recitation portion and the final exams (written and oral).

Practical placement

None

Bibliography

Can change depending on the lecturer.

Additional information

Additional information (registration calendar, class conductors, localization and schedules of classes), might be available in the USOSweb system:

Description of 1102-301A in USOSweb