COURSE REQUIREMENTS

• Title: Modern solid state physics
• Major: Physics MSc of FNS BME
• Neptun Code: BMETE11MF55
• Requirement: 3/2/0/V/7
• Prerequisite: BSc Diploma in Physics
• Language: english
• Lecturer: Dr. Attila Virosztek (course T0);
• Practical course: Dr. Balázs Hetényi (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: 6th week (on practice); retake: 13th week. Topics: identical particles, second quantization for bosons and fermions, field operators, phonons, magnons, bosons.
  • 2. test: 12th week (on practice); retake: 13th week. Topics: Fermi liquid, Hartree-Fock approximation, Wigner crystal, Wannier states, Hubbard model.
  • Both tests can be attempted on the 13th 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 proposed 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 proposed by one unit only. Those having signature from a previous semester will be offered the same grade as was proposed in that previous semester.
• Consultations (upon request):
  • wednesday 15:15-16:00; educator: Dr. Balázs Hetényi
  • thursday 8:15-9:00; educator: Dr. Attila Virosztek

PROBLEM SET

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, electron-phonon interaction, Wannier basis, one band Hubbard modell.

Ferromagnetism of metals

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.

Susceptibility of metals

Electric and magnetic perturbations, time dependence of operators, dynamic susceptibility of interacting electrons in mean field approximation, spectrum of excitations, collective modes.

Screening, Hartree-Fock 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 Hartree-Fock approximation, Wigner crystal.

Spin density waves

Static susceptibility, quasi-one 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