Description:

The lecture describes the birth of quantum mechanics and description of one particle and more particles by elements of the Hilbert space as well as its time evolution. Besides that it includes description of observable quantities by operators in the Hilbert space and calculation of their spectra.

Contents:

1. Experiments leading to the birth of QM
2. De Broglie's conjecture, Schroedinger's equation
3. Description of states and observables in QM
4. Elements of Hilbert space theory and operators
5. Measurement in quantum mechanics, transition probabilities
6. Spin-1/2 particle
7. Linear harmonic oscillator
8. Quantization of angular momentum
9. Particle in a spherical potential ? isotropic oscillator, Coulomb field
10. Position and momentum
11. Mean values of observables and transition probabilities, uncertainty relations
12. Time evolution of states

Seminar contents:

1. Summary of classical hamiltonian mechanics, statistical physics and probability theory
2. De Broglie waves
3. Particle in an infinite square well, spin-1/2 particle
4. Linear harmonic oscillator
5. Orbital angular momentum
6. Predictions of measurement outcomes, mean values of observables, uncertainty relations
7. Time evolution in quantum mechanics
8. Free particle, spreading of the wave-packet

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