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Quantum Mechanics

Blackbody radiation, photoelectric effect, Compton effect, stability and line spectra of atoms Frank-Hertz experiment, Time dependent and independent Schrödinger's equation, stationary states, wave function. "wave - particle duality", electron diffraction, two-slit experiment, uncertainty relations, electron wavefunction probability distribution in an atom, solving the Schrödinger equation, tunneling,the ammonia molecule,electron emission from metals, perturbation calculus. selection rules, operator calculu,.eigenstate problems,measurement quantum mechanics the hydrogen atom., quantum numbers, H spectrum and selection rules, electron spin, Zeeman-effect, Stern-Gerlach experiment, spin-orbit coupling, atoms with more than one electron, the exclusion principle, indistinguishable particles, periodic table of elements, buildup of shells, Hund's rule, valence and core electrons. Molecules. molecular orbitals, chemical bonding, H-H bond, H2+ molecule ion, bonding and anti-bonding states, orbital hybridisation, heteronuclear molecules, sp3 hybridization, rotation and vibration of molecules, Franck-Condon principle, Rayleigh and Raman scattering, Stokes and anti-Stokes scattering, Statistical physics. Classical and quantum statistics. Distribution functions, distinguishable and undistinguishable particles, photon gas, Einstein model, laser principle

Solid State Physics

Short and long range ordering, amorphous and crystalline solids, crystal structures, lattices. (point lattice and basis), symmetries and unit cells, primitive,conventional and Wigner-Seitz cells, primitive vectors, Miller indexes, Bravais lattices, close packing structures, reciprocal lattice, k-space, X- ray diffraction,, Laue formulae, classical physical models for crystals: lattice vibrations, monatomic and diatomic linear chain model, boundary conditions, form of the solution, dispersion relation, generalization for 3 dim., QM handling of lattice vibrations, phonos, momentum and energy of phonons, relative to the momentum and energy of Bloch electrons, specific heat of solids, equipartition principle and the Debye model, specific heat from electrons, conductors and insulators, band theory of solids, formation of bands, insulators, conductors, real band structures, conduction models, Drude model, collision time, mean free path, Wiedmann-Franz law, Sommerfeld model of metals, Fermi energy, , electrons and holes,, equivalence of electron and hole conductivity in a completely filled band, metals with hole conduction, work function, thermionic emission, contact potential, crystal potential, double layer at the surface,, Bloch functions, Hartree-Fock method, dispersion relation, Brillouin zone, reduced zone picture, kinematics of electrons and holes, Bloch oscillations, effective mass, tight binding model, semiconductors, intrinsic conductivity, , density of states in the conduction and valence bands, position of the Fermi level, donors and acceptors, charge carrier concentrations, extrinsic conductivity, Fermi level in doped semiconductors, p-n junction,application of p-n junctions., diode, (MOS)FET, bipolar transistors, Schottky and ohmic structures, characteristics.

Quantum Mechanics - Prof. Dr. P. I. Richter

Solid State Physics - Prof. Dr. A. I. Sólyom

There will be 2 written tests during the term, one for each topics. You must earn at least 20 of the 50 points on each test to pass. Each test contains 10 quiz questions and 3 numerical problems.
The tests are close book. You may use only your calculator.

You must pass these tests to have a successful semester (i.e. get a signature for it so that you can enroll a cross-semester if you failed to participate in or pass the exams), but to get graded you must take the final (on-line verbal) exam.

There will also be one makeup tests for both Quantum Mechanics and Solid State Physics for those who failed on or; for some reason; missed any of the previous tests. You must sign up for those held in the makeup week in Neptun, but they are free. 2 more makeup tests will be held for those who still will not have had enough points, but those requires you to pay a fine fro them.

The results of the tests may slightly modify the final score on the exam, but yje exam is independant of the test results (if you have at least 20 point on both tests). On the exam it is possible (it never happened though) to fail even with two perfect tests or excel with tests of minimum points (yes, I would be happy too if you do that).

Example problems are in the course material and under Example Problems below.

There are no test results yet in this semester

These theoretical questions, from which 5 will be asked during the examinations, can be answered with one short sentence. See General Information below.

To get to the oral examination you must answer at least 3 of 5 "must know" questions. Failed to meet this criterion means a failed exam. (with mark 1)!

On exams only those "Must Know" questions will be asked that are covered in the actual semester.

Quantum Mechanics

1. What device is the spectrometer?
2. Value and unit of the elementary charge and of 1 electron volt
3. Value of the thermal energy at room temperature in electron volts
4. Value and unit of the Planck constant
5. What is a wave vector?
6. de Broglie wavelength formula, momentum expressed with the wave vector
7. How can the energy of a physical system change in classical physics and in quantum mechanics? What about electromagnetic waves?
8. When do we need to use quantum mechanics instead of classical physics?
9. What quantity is called ``potential' in quantum mechanics?
10. Particle-wave duality and what it means
11. What is the wave function?
12. Commutators and Uncertainty Relations between p and r; t and E; L_x, L_y and L_z
13. What is the Density of States?
14. Write up both the time dependent and stationary Schr"odinger equations in one dimension!
15. Difference of the classical orbit and the QM orbital of an electron
16. Give definition of the operators for p and r (or x)
17. State both variations of the Pauli principle
18. What is the Boltzman factor?
19. What are the statistical energy distributions formulas?
20. In which conditions do we need to use quantum statistics?
21. When should the Maxwell-Boltzmann (M-B) energy distributions formula be applied?
22. When should the Bose-Einstein (B-E) energy distributions formula be applied?
23. When should the Fermi-Dirac (F-D) energy distributions formula be applied?

Solid State Physics

1. Define short range ordering
2. Define long range ordering
3. What are solids?
4. What are crystals?
5. What are cells in a crystal?
6. What are primitive cells?
7. What are conventional unit cells?
8. What is a point lattice?
9. What is the basis?
10. What is a Bravais lattice
11. What kind of symmetry must all crystals have?
12. What is a reciprocal lattice?
13. What is the dispersion relation for electrons?
14. What is the dispersion relation for phonons?
15. What solids are called conductors?
16. What solids are calledinsulators?
17. What are semiconductors?
18. Differential Ohm's law formula
19. Define the crystal momentum of Bloch electrons
20. Define the mobility of charge carriers
21. What is the Fermi energy in metals?
22. What is the Fermi energy in insulators and intrinsic semiconductors?
23. Give the effective mass formula in 1D!
24. Give the effective mass formula in 3D!
25. What are holes?
26. Can you use both holes and electrons together to describe conduction in metals?
27. Can you use both holes and electrons together to describe conduction in semiconductors?
28. What are majority charge carriers?
29. What are minority charge carriers?
30. How can we measure the sign of the majority charge carriers?
31. What are the space charge region and the depletion region?
32. What is the p-n junction?
33. What type of metal-semiconductor junction are used?

Answers to the "Must Know" questions

At the end of the term Student performance is measured in oral examinations.

Only those with 2 successful tests can partake in the examination. The result of the tests may modify the final score on the exam, but on the exam it is possible (although unlikely) to fail even with two perfect tests or excel (this is slightly more probable) even with tests of only minimum points.

Main goal of the examination is to ascertain the understanding of the physics behind the formulae and not the formulae themselves. Even with topics which are about some example problems you need not perform a full mathematical solution. You may do it if you like, of course, but it is enough to give a description what should be done to solve the problem and what are the characteristics of the solution. However, the knowledge of some basic constants and formulae (for example Schrödinger equations) is still required - see the What you MUST know... section for those).

To get to the oral examination you must answer at least 3 of 5 "must know" questions. Failed to meet this criterion means a failed exam. (with mark 1)!

On exams only those "Must Know" questions will be asked that are covered in the actual semester.

Each student has 25 minutes to talk about the topics (1 topic from QM, and 1 from SSF), selected from the topics below by a random number generator. No two persons will be given the same topics on the same day.

The list of topics below may change during the semester and will reflect topics only that were actually covered during the semester.

As examination time is limited, please try to be as concise as you can!

Everyone will get one question for Quantum Mechanics and one for Solid State Physics from the list of topics below selected on the day of the exam by a random number generator. No two persons will be given the same topics on the same day.

Quantum Mechanics

1. Experimental antecedents
   
   Blackbody radiation, photoelectric effect, Compton effect, stability and line spectra of atoms, Frank-Hertz experiment, why can't you explain these in classical physics?
2. Time independent Schrödinger's equation, stationary states
   
   Intuitive 'derivation', solutions, free electron, superposition
3. Time dependent Schrödinger's equation
   
   'Derivation', Connection to the time independent equation, general solution as a linear combination, non stationary states, example time dependent wave functions in a potential box
4. The Wave function. Wave - particle duality
   
   De Broglie, Electron diffraction, thought experiments (two-slit, self-interacting wave) wave packet, uncertainty relations, electron wavefunction probability distribution in an atom
5. Simple problems #1: 1. dim. potential step
   
   Form of the equation in different regions, trial form of solutions, boundary conditions, solution
6. Simple problems #2: Potential box in 1D
   
   Form of the equation in different regions, trial form of solutions, boundary conditions, solution, scalar product and ortonormality of eigenfunctions, ground state
7. Simple problems #3: Potential box in 3D
   
   Form of the solution, Degeneracy of levels. Orthoganality for degenerate levels, Density of states in 3D.
8. Simple problems #4: 1. dim. potential well
   
   Form of the equation in different regions, trial form of solutions, boundary conditions, solution
9. Simple problems #5: 1 dim. linear harmonic oscillator
   
   Form of the equation, properties of the solution, energy, wave functions and probability densities.
10. Tunneling
    
    Model potential, qualitative solution, discussion of the results. The ammonia molecule. Electron emission from metals
11. Perturbation calculus. Selection rules.
    
    Non stationary states, time dependent and time independent perturbations, transition probabilities, successive approximation, selection rules in linear harmonic oscillators.
12. Formal quantum mechanics. I. Operator calculus.
    
    Selection and mathematical properties of quantum mechanical operators. Mathematical form of operators of position and momentum, commutators
13. Formal quantum mechanics. II. Regular functions. Eigenstate problems.
    
    regular functions. eigenstates and eigenvalues.
14. Measurement in formal quantum mechanics
    
    Measurements in quantum mechanics, commutators, canonical conjugates and uncertainty relations, co-measurement of physical quantities.
15. Angular momentum. The hydrogen atom.
    
    The operators of angular momentum, conservation law, uncertainty of angular momentum components L_z and its eigenfunctions and eigenvalues in spherical polar coordinates
16. The hydrogen atom.
    
    Schrödinger equation in central potentials, separation of the wave function to radial and angular part, quantum numbers.
17. H spectrum and selection rules
    
    Transitions in H, Bohr model, Balmer formula, selction rules, spherical harmonics.
18. Zeeman-effect, the electron spin
    
    Magnetic momentum of electrons in an atom, Zeeman-effect, Stern-Gerlach experiment, spin-orbit coupling
19. The He atom, the independent particle approximation.
    
    Atoms with more than one electron, models for the He atom, approximations, application of perturbation theory
20. The exclusion principle.
    
    Indistinguishable particles, symmetric and antisymmetric wave functions, singlet and triplet states, example - the He gas. Equivalent formulations of the Pauli principle.
21. Periodic table of elements
    
    Periodicity in physical and chemical properties, angular momentum in atoms, buildup of shells Hund's rule, valence and core electrons
22. Molecules. molecular orbitals, chemical bonding, H-H bond
    
    H₂⁺ molecule ion, bonding and anti-bonding states, homonuclear molecules, sigma and pi bonds, chemical bonding, the H-H molecule
23. Chemical bonding, Molecules of many atoms. Orbital hybridisation
    
    heteronuclear molecules, chemical bonds, covalent and ionic bonding, multiatomic molecules, H₂O molecule, hydrocarbon molecules, sp³ hybridization.
24. Rotation and vibration of molecules.
    
    Angular momentum of molecules, momentum of inertia, selection rules, vibration, normal modes for multiatomic molecules
25. Franck-Condon principle, Rayleigh and Raman scattering
    
    Elastic and inelastic scattering of EM radiation by particles much smaller than the wavelength, Stokes and anti-Stokes scattering
26. Statistical physics. Classical statistics. Distribution functions
    
    Purpose, statistical equilibrium, distinguishable and undistinguishable particles,M-B distribution functions.
27. Quantum statistics. Distribution functions
    
    Distinguishable and undistinguishable particles, F-D,B-E statistics and distribution functions, distribution function comparision
28. Interaction of light and matter. Photon gas
    
    Equilibrium between light and matter, average energy, density of states, 'photon gas', Einstein model, Laser principle

Solid State Physics

1. Different types of solids. Short and long range ordering.
   
   Definition of a solid, amorphous and crystalline solids, short range ordering, long range ordering
2. Crystal structures. Lattices. (point lattice and basis). Symmetries and Unit cells
   
   Geometrical description of crystals. Base symmetry of all crystals, primitive, conventional and Wigner-Seitz cells, primitive vectors.
3. Symmetries, Miller indexes
   
   Symmetries, possible symmetries for crystals planes and directions, Miller indices.
4. Bravais lattices. Reciprocal lattice.
   
   Definition and symmetries of Bravais lattices. Close packing structures Definitions of the reciprocal lattice, k-space, Brillouin zone, what is the reciprocal lattice of fcc, bcc and sc lattices.
5. Determination of crystal lattices. I. X- ray diffraction Bragg condition
   
   X-ray diffraction, Bragg model, Derivation of Bragg's formula, drawbacks.
6. Determination of crystal lattices. II. X- ray diffraction Laue formulas
   
   X-ray diffraction and reciprocal lattice. Derivation of the Laue equations,geometrical structure factor
7. Classical physical models for crystals: lattice vibrations. I. 1D monatomic bases
   
   Equations for the monatomic linear chain model, boundary conditions, form of the solution, dispersion relation.
8. Classical physical models for crystals: lattice vibrations. II. 1D diatomic bases. Generalization for 3 dim.
   
   Equations for the diatomic linear chain models, boundary conditions, form of the solution, dispersion relation, branches in 1 and 3D.
9. QM handling of lattice vibrations
   
   How to go from classical models to QM models, Phonos. Momentum and energy of phonons, relative to the momentum and energy of Bloch electrons (no need to define what a Bloch electron is.)
10. Specific heat of solids
    
    Definition of specific heat. Temperature dependence, equipartition principle and the Debye model. Specific heat from electrons
11. Conductors and insulators. Band theory of solids.
    
    Schematic band picture, formation of bands, insulators, conductors, real band structures
12. The Drude model and its shortcomings
    
    Assumptions of the Drude model, collision time, mean free path, methods of determination of τ, Wiedmann-Franz law, failures of the model
13. Nearly free electron model: Sommerfeld model of metals.
    
    Assumptions, Fermi energy, specific heat, electrical conductivity
14. Electrons and holes
    
    Current of full bands. Current of electrons. Current of holes. Equivalence of electron and hole conductivity in a completely filled band. Metals with hole conduction.
15. Work function. Thermionic emission. Contact potential. Measurement methods
    
    Model of the crystal potential, double layer at the surface, potential at different faces, neutrality, characteristics of thermionic emission, contact potential and its measurement.
16. Electrons in periodic lattices. Brillouin-zone. Bloch functions
    
    Schrödinger equation, adiabatic principle, Hartree-Fock method, Bloch functions
17. Crystal momentum of Bloch electrons. Dispersion relations.
    
    Calculation of momentum, crystal momentum, kinetic energy and crystal momentum,Determination of u(x), dispersion relation, Brillouin zone, reduced zone picture.
18. Kinematics of electrons and holes. Bloch oscillations. Effective mass.
    
    The effect of a constant external electric field, velocity and acceleration in the Brillouin zone in 1D, dispersion relations in 3D, effective mass in 1D and 3D, holes, hole and electron effective masses
19. Tight binding model. Width of the energy bands
    
    Assumptions of the model, Delocalised Bloch electrons from localized wave functions, band width calculation
20. Homogeneous semiconductors. I. Intrinsic semiconductors
    
    Semiconductors, intrinsic conductivity, electrons and holes in intrinsic semiconductors, charge carrier concentrations, the law of mass action, density of states in the conduction and valence bands, position of the Fermi level
21. Homogeneous semiconductors. II. Extrinsic semiconductors. Donors and acceptors
    
    Charge carrier concentrations, extrinsic conductivity, electrons and holes, the law of mass action, donor and acceptor atoms, density of states in the conduction and valence bands, Fermi level in doped semiconductors.
22. Semiconductor structures. I. The p-n junction.
    
    Inhomogeneous semiconductor structures, unbiased and biased p-n junction, what are generation and recombination currents voltage characteristics
23. Semiconductor structures. II. Application of p-n junctions.
    
    Rectification, current-voltage characteristics, diode, (MOS)FET, bipolar transistors
24. Smiconductor-metal structures
    
    Rectifying (Schottky) and ohmic junctions, characteristics
25. Emission and absorption of visible light. Luminescence and phosphorescence.
    
    Transparency for visible light, color of materials, immediate and delayed interband transitions, causes of luminescence.
26. Optical properties. X-ray emission and absorption.
    
    Atomic and interband transitions, schematic soft X-ray spectra, X-ray absorption in metals, insulators, intrinsic and doped semiconductors