Talk:NSU PHD Qualifying Exam
Topics and Sample Questions for Oral Exam for PhD Qualifiers – 1/26/09
Mathematics
1. Algebra, inversely and directly proportional, basic functions of one and two variables and their graphical representation.
2. Derivatives and integrals of common functions. Definition and application of differentials and derivatives.
3. Complex numbers: transformation between Cartesian and polar forms. Argand’s plane representation.
4. Basic Concepts of Linear Algebra: Vector and Matrix operations, determinants
Physics
1. Explain the law of conservation of energy; kinetic and potential energies; work and heat.
2. Know the ideal Gas Laws, and their assumptions. Absolute Temperature and change of temperature units.
3. Know the First and Second Laws of Thermodynamics. Heat, and how it relates to heat capacity, phase transformations, and change in temperature.
4. Know the definition and basic equations related to Electric field and Electric Potential, Coulomb’s law, Gauss's law, Dielectrics and polarization, Maxwell equations.
5. Explain and use in conceptual problems: polarization, interference, diffraction.(Basics of Light)
6. Electromagnetic spectrum: relationship between frequency, energy and wavelength; classification of different parts of the electromagnetic spectrum, and interaction of electromagnetic radiation with matter, depending on the radiation wavelength. (Electromagnetic Spectrum)
Elementary Quantum Physics
Know the basic concepts, and basic equations related to:
1. Wave-particle dualism
2. Blackbody Radiation
3. Photoelectric effect
4. Plank, De Broglie, Einstein relations (dispersion relations for particles with the mass and photons)
5. Schrödinger equation
6. “Particle in the box”, harmonic oscillator
7. Uncertainty relations (momentum-position, time-energy)
8. Barriers, tunneling
9. Electronic structure of hydrogenic atom
10. Spin, angular momentum
11. Fermi’s golden rule
Chemistry and Polymers
1. Identify and define: materials, atoms and ions, sub-atomic particles, elements and isotopes.
2. Understand the periodic table and its arrangement: atomic numbers, atomic weight, and general chemical and physical properties of the elements, periodic properties. (Molecular Orbitals)
3. Differentiate between the structure and properties of metals, non-metals, inorganic materials, organic materials, polymers, ceramics, and composites; crystalline and amorphous materials.
4. Know the chemical structure, molecular formula, classification and how to calculate molecular weights of common organic and inorganic compounds (acids, based, oxides, salts)
5. Define oxidizers, reducers, and oxidation-reduction reactions
6. Key types of organic compounds and functional groups, properties, reactions, and applications
7. Basic polymer forming reaction methods, biological and inorganic polymers
8. Polymer molecular weights, morphology, structure-property relationships (Electronic Band Structure of Organic Materials)
9. Electronic and Optoelectronic Polymers and Applications: definition, explain structure-property relationship (Structure-Property Relationships) (Passive Optical Polymers) (Electro-optic Polymers and Devices)
Materials Science, Electronic and Photonic Materials
1. Crystal Structure: Directions and planes
2. Lattice vibrations: Acoustical and optical branches; phonons
3. Thermal properties: Specific heats. Thermal expansion, Thermal conductivity
4. Diffusion, Fick’s Laws
5. Mechanical behavior. Plastic and elastic deformations. Young’s modulus
6. Phases, phase diagram. One component and binary systems. The Gibbs Phase rule.
7. Magnetic Properties. Basic concepts. Magnetic moment and permeability. Paramagnetic, ferromagnetic, antiferromagnetic materials
8. Electrical properties of metals and semiconductors. Hall effect. Intrinsic and extrinsic semiconductors; electrons and holes, electrical conductivity, statistics of electrons and holes, recombination and injection, life-time. (Electrical Properties) (Transport)
9. Electric permittivity and susceptibility in dielectrics (Lorentz model) and in metals (Drude model).Freederickz Transition and Dielectric Anisotropy
10. Basics of semiconductor devices. Concept of p-n junction, Schottky junction and its electronic properties, MOS structure and basics of the field-effect, structure and operation principles of the bipolar transistors, basics of photonics devices (LED, photodetectors, solar cells, semiconductor lasers) (Electro Optical Components)(What is a Light Emitting)Diode?) (Organic Solar Cells)
11. Basic methods and principles for materials characterization: Optical spectroscopy (X-ray, UV-visible, IR, Raman), Electron spectroscopy, Magnetic resonance spectroscopy (NMR, ESR).
12. Refraction, reflection, and transmission in loss-less dielectrics: index of refraction, Snell’s law, Brewster angle, total internal reflection, Frensel formulas for reflection and transmission. (Basics of Light )
13. Electric permittivity and susceptibility in dielectrics (Lorentz model) and in metals (Drude model). Classical and quantum approaches to absorption in materials.
14. Basics of laser materials: principles of operation (Lasers)