COURSE REQUIREMENTS

Title: Modern solid state physics

Major: Physics MSc of FNS BME

Neptun Code: BMETE11MF55

Requirement: 3/2/0/V/7

Language: english

Lecturer: Dr. Attila Virosztek (course T0);

Practical course: Károly Nagy (course T1);

Attendance: Presence on at least 50% of the lectures and at least 70% of the practices is required for signature. Absence is recorded on each occasion.

Tests during the semester: twice (90 minutes, 40 points each).

1. test: 9th week (on practice); second chance: 15th week. Topics: identical particles, second quantization for bosons and fermions, field operators, phonons, magnons, bosons.

2. test: 14th week (on practice); second chance: 15th week. Topics: Fermi liquid, HartreeFock approximation, Wigner crystal, Wannier states, Hubbard model.

Both tests can be attempted on the 15th week. If still unsuccessful, there is a third possibility, but special process charge applies.

Requirements for signature – besides proper attendance –, both tests should be successful (at least 40% each).

Grades are offered based on the sum of points earned at the two tests:

from 0% to 39%: fail (1)

from 40% to 54%: pass (2)

from 55% to 69%: satisfactory (3)

from 70% to 84%: good (4)

from 85% to 100%: excellent (5)

Those who do not accept the grade offered, may take oral exam. This can result in a final grade which differs from the one offered by one unit only. Those having signature from a previous semester will be offered the same grade as was offered in that previous semester.

Consultations:

wednesday 15:1516:00; educator: Károly Nagy

thursday 11:1512:00; educator: Dr. Attila Virosztek
TOPICS
Identical particles
Many particle wavefunction, symmetrization, Slater determinant, particle number representation.
Second quantization
Second quantized form of one and two particle operators, creation and annihilation operators, commutation relations, field operators.
Interacting electron system
Second quantized form of the Hamiltonian of free and Bloch electrons, electronphonon interaction, Wannier basis, one band Hubbard modell.
Zeeman energy, homogeneous susceptibility of noninteracting system, mean field approximation, Stoner formula, lifetime of interacting electrons.
Linear response theory
Kubo formula in real space, and in Fourier space.
Electric and magnetic perturbations, time dependence of operators, dynamic susceptibility of interacting electrons in mean field approximation, spectrum of excitations, collective modes.
Screening, HartreeFock approximation
Screening of a point charge, induced charge, Friedel oscillations, Kohn anomaly, dynamic screening, plasmon oscillations, reflectivity of metals, interacting free electron spectrum, metallic bonding, region of applicability of the HartreeFock approximation, Wigner crystal.
Spin density waves
Static susceptibility, quasione dimensional system, nesting, SDW instability, diagonalization of the mean field Hamiltonian below the critical temperature, quasiparticles, gap equation, specific heat jump.
Bose liquid
Bose condensation, ground state of weakly interacting bosons, determination of the spectrum of excitations by Bogoliubov transformation, superfluidity.
LITERATURE (for second quantization)
Landau III. Nonrelativistic quantummechanics, chapter IX. (Identical particles); Abrikosov, Gorkov, Dzyaloshinski: Methods of quantum field theory in statistical physics, Chapter 3. Second quantization
PREREQUISITS:
Quantummechanics, Solid state physics, Statistical physics