Description:

The lecture expands the introduction to quantum mechanics with more general formalism of quantum theory or approximate methods.

Contents:

1. Dirac formalism
2. Linear harmonic oscillator, creation and annihilation operators
3. Particle in the electromagnetic field, spin of an electron
4. Zeeman effect
5. Algebraic theory of angular momentum
6. Time independent perturbation methods
7. Stark effect
8. Many particle systems
9. Potential scattering, tunneling phenomenon
10. Density matrix

Seminar contents:

1. Linear harmonic oscillator, creation and annihilation operators
2. Spin-1/2 in homogeneous magnetic field
3. First and second order perturbation corrections
4. Ritz variation method for a helium atom.
5. Density matrix of a two-level system, thermal state of a harmonic oscillator, Gibbs state.

Recommended literature:

Key references:
[1] P.A.M. Dirac, Principles of Quantum Mechanics, Oxford University Press, Oxford 1958.

Recommended references:
[2] L. D. Faddeev and O. A. Yakubovskii: Lectures on Quantum Mechanics for Mathematics Students (Student Mathematical Library), AMS 2009.
[3] K. Gottfried, T. Yan: Quantum mechanics: Fundamentals, Springer, 2013.

Keywords:

quantum mechanics; Hilbert space; wave function; probability prediction

Abbreviations used:

Semester:

• W ... winter semester (usually October - February)
• S ... spring semester (usually March - June)
• W,S ... both semesters

Mode of completion of the course:

• A ... Assessment (no grade is given to this course but credits are awarded. You will receive only P (Passed) of F (Failed) and number of credits)
• GA ... Graded Assessment (a grade is awarded for this course)
• EX ... Examination (a grade is awarded for this course)
• A, EX ... Examination (the award of Assessment is a precondition for taking the Examination in the given subject, a grade is awarded for this course)

Weekly load (hours per week):

• P ... lecture
• C ... seminar
• L ... laboratory
• R ... proseminar
• S ... seminar