Course title:

Advanced Quantum Physics

Primary programme:

Fizikus mérnök BSc

ECTS credits:

3

Course type:

elective

Number of lectures per week:

2

Number of practices per week:

0

Number of laboratory exercises per week:

0

Further knowledge transfer methods:

Grading:

Examination

Special grading methods:

Semester:

6

Prerequisites:

Modern physics

Responsible lecturer:

Dr. András Pályi, univ. associate professor, PhD

Lecturers and instructors:

Course description:

This course gives a deeper insight into quantum mechanics, beyond that of a freshman course. The course builds upon the worldwide extensively used book of Griffiths.
The Schrödinger wave function: The Schrödinger equation, probability, probability current.
The time-independent Schrödinger equation (2 lectures): Stationary states; the infinite square well; harmonic oscillator: algebraic method. The free particle, motion of Gaussian wave packet; bound states and scattering states: the finite square well.
The formalism of quantum mechanics: Hilbert space, vectors and operators; observables as Hermitian operators; eigenfunctions of a Hermitian operators; bases in Hilbert space, Dirac notation.
Quantum mechanics and angular momentum (2 lectures): the radial Schrödinger equation, the hydrogen atom, the radial wave function, the spectrum of hydrogen. Angular momentum: algebraic treatment, eigenvalues, eigenfunctions. Spin, spin 1/2, addition of spins.
Time-independent perturbation theory (2 lectures): Non-degenerate first-order perturbation theory, second-order energies degenerate perturbation theory. Applications: the Zeeman effect, Stark effect, the hyperfine structure of hydrogen.
The variational principle: Theory; harmonic oscillator, anharmonic oscillator, hydrogen ground state; the ground state of Helium.
Quantum dynamics (2 lectures): Two-level systems, the perturbed system, time-dependent perturbation theory, Rabi oscillations. Emission and absorption of radiation, the lifetime of an excited state, Fermi’s golden rule, selection rules.
Scattering (2 lectures): Classical scattering theory, quantum scattering theory and partial wave analysis, phase shifts. The Lippmann-Schwinger equation, the first Born approximation, Coulomb scattering.
Identical particles: Two-particle systems, bosons and fermions, Pauli principle, hydrogen molecule.
Quantum mechanical pictures: Heisenberg picture, interaction picture.

Reading materials:

D.J. Griffiths and D.F. Schroeter: Introduction to Quantum Mechanics (Cambridge Univ. Press, 2018, ISBN: 978-1107189638 )
J.J. Sakurai and Jim Napolitano: Modern Quantum Mechanics (Cambridge Univ. Press 2021, ISBN: 978-1108473224)

List of competences:

Please find the detailed list, as quoted from the Hungarian training and outcome requirements of the Physicist Engineer program, in the Hungarian version of the course description.