Problems

• Crystal Structures
  • Problem: Symmetries
  • Problem: Rotations
  • Problem: Copper Oxide Layers
  • Problem: Graphite
  • Problem: Structure of A C
  • Problem: hcp and fcc Structures
  • Problem: hcp and bcc Structures
  • Problem: Structure Factor of A C
  • Problem: Neutron Diffraction Device
  • Problem: Linear Array of Emitters, Finite Size Effects
  • Problem: Linear Array of Emitters, Superlattice
  • Problem: Powder Diffraction of hcp and fcc Crystals
  • Problem: Momentum Resolution
  • Problem: Finite Size Effects
  • Problem: Random Displacement
  • Problem: Vacancies
  • Problem: Integrated Scattering Intensity
• Interatomic Forces, Lattice Vibrations
  • Problem: Madelung Constant
  • Problem: NaCl Bulk Modulus
  • Problem: Madelung with Screened Potential
  • Problem: Triple-axis Spectrometer
  • Problem: Phonons in Silicon
  • Problem: Linear Array of Emitters, Phonons
  • Problem: Long Range Interaction
  • Problem: Mass Defect
  • Problem: Debye Frequency
  • Problem: Vibrations of a Square Lattice
  • Problem: Grüneisen Parameter
  • Problem: Diatomic Chain
  • Problem: Damped Oscillation
  • Problem: Two-Dimensional Debye
  • Problem: Soft Optical Phonons
  • Problem: Soft Phonons Again
• Electronic Band Structure
  • Problem: Nearly Free Electrons in One Dimension
  • Problem: Nearly Free Electrons in Dirac-Delta Potentials
  • Problem: Tight-Binding in Dirac-Delta Potentials
  • Problem: Dirac-Delta Potentials
  • Problem: Band Overlap
  • Problem: Nearly Free Electrons in Two Dimensions
  • Problem: Nearly Free Electron Bands
  • Problem: Instability at the Fermi Wavenumber
  • Problem: Electrons in 2D Nearly Free Electron Band
  • Problem: Square Lattice
  • Problem: Tight-Binding Band in Two Dimensions
  • Problem: Electrons in 2D Tight-Binding Band
  • Problem: Dirac-Delta Potentials in Two Dimensions
  • Problem: Effective Mass
  • Problem: Cyclotron Frequency
  • Problem: de Haas-van Alphen
  • Problem: Fermi Energy
• Density of States
  • Problem: Density of States
  • Problem: Two-Dimensional Density of States
  • Problem: Two-Dimensional Tight-Binding
  • Problem: Quasi-One-Dimensional Metal
  • Problem: Crossover to Quasi-One-Dimensional Metal
  • Problem: Phonon Mode of Two-Dimensional System
  • Problem: Saddle Point
  • Problem: Density of States in Superconductors
  • Problem: Energy Gap
  • Problem: Density of States for Hybridized Bands
  • Problem: Infinite-Dimensional DOS
  • Problem: Two-Dimensional Electron Gas
• Elementary Excitations
  • Problem: Tight-Binding Model
  • Problem: Hybridization of Energy Bands
  • Problem: Polarons
  • Problem: Polaritons
  • Problem: Excitons
  • Problem: Holstein-Primakoff Transformation
  • Problem: Dyson-Maleev Representation
  • Problem: Spin Waves
  • Problem: Spin Waves Again
  • Problem: Anisotropic Heisenberg Model
  • Problem: Solitons
• Thermodynamics of Noninteracting Quasiparticles
  • Problem: Specific Heat of Metals and Insulators
  • Problem: Number of Phonons
  • Problem: Energy of the Phonon Gas
  • Problem: Bulk Modulus of Phonon Gas
  • Problem: Phonons in One Dimension
  • Problem: Electron-Hole Symmetry
  • Problem: Entropy of the Noninteracting Electron Gas
  • Problem: Free Energy with Gap at the Fermi Energy
  • Problem: Bulk Modulus at T=0
  • Problem: Temperature Dependence of the Bulk Modulus
  • Problem: Chemical Potential of the Free-Electron Gas
  • Problem: EuO Specific Heat
  • Problem: Magnetization at Low Temperatures
  • Problem: Electronic Specific Heat
  • Problem: Quantum Hall Effect
• Transport Properties
  • Problem: Temperature Dependent Resistance
  • Problem: Conductivity Tensor
  • Problem: Montgomery Method
  • Problem: Anisotropic Layer
  • Problem: Two-Charge-Carrier Drude Model
  • Problem: Thermal Conductivity
  • Problem: Residual Resistivity
  • Problem: Electric and Heat Transport
  • Problem: Conductivity of Tight-Binding Band
  • Problem: Hall Effect in Two-Dimensional Metals
  • Problem: Free-Electron Results from the Boltzmann Equations
  • Problem: p-n Junctions
• Optical Properties
  • Problem: Fourier Transform Infrared Spectroscopy
  • Problem: Optical Mode of KBr
  • Problem: Direct-Gap Semiconductor
  • Problem: Inversion Symmetry
  • Problem: Frequency-Dependent Conductivity
  • Problem: Frequency-Dependent Response of a Superconductor
  • Problem: Transmission of a Thin Superconductor
  • Problem: Bloch Oscillations
• Interactions and Phase Transitions
  • Problem: Spontaneous Polarization
  • Problem: Divergent Susceptibility
  • Problem: Large-U Hubbard Model
  • Problem: Infinite Range Hubbard Model
  • Problem: Stoner Model
  • Problem: One-Dimensional Electron System
  • Problem: Peierls Distortion
  • Problem: Singularity at
  • Problem: Susceptibility of a One-Dimensional Electron Gas
  • Problem: Critical Temperature in Mean Field Approximation
  • Problem: Screening of an Impurity Charge
  • Problem: Fermi Surface Nesting in Two Dimensions
  • Problem: Fermi Surface Nesting in Quasi One Dimension
  • Problem: Anderson Model