Course Identification

מכניקה קוונטית לתוכנית רוטשילד-וייצמן
מכניקה סטטיסטית לתוכנית רוטשילד-וייצמן

I. The Fundamentals

1. Introduction
1.1 Why Majority of Solids are Crystalline?
1.1.1 Simple System of Point Like Particles with van der Vaals Interactions
1.1.2 Temperature Effects
1.1.3 Quantum Mechanical Effects
1.1.4 More Realistic Systems
1.2 Condensed Matter Which is Not Crystaline
1.2.1 Long Range Order
1.2.2 Glasses, Polymers, Liquid Crystals and Quasicrystals

2. Description of Crystal Lattices
2.1 Lattices of Points. Bravais Lattices
2.2 Realistic Lattices. Lattices with Bases. Examples.
2.3 Classification of Bravais Lattices
2.4 Unit Cell
2.5 The Reciprocal Lattice. First Brillouin Zone
2.5.1 The Definition
2.5.2 The Reciprocal Lattice is a Bravais Lattice Too
2.5.3 First Brillouin Zone
2.6 Experimental Determination of Lattice Structure.
2.6.1 X-ray Diffraction
2.6.2 Diffraction off Atomic Lattice
2.6.3 Discussion. Laue Conditions for Bragg Peaks

3. Electronic Structure 22
3.1 Simple Model of Simple Crystals
3.2 The Periodic Potential
3.3 Bloch Theorem. Electronic Bands
3.4 Nearly Free Electron Model
3.4.1 Qualitative arguments
3.4.2 Solving the Schrodinger Equation
3.5 Examples of Calculated Energy Bands
3.6 How Many Electrons Can a Band Accommodate. The Fermi Level               
3.7 Metals, Semiconductors and Insulators
3.8 How are Electronic Bands Related to the Original Atomic Levels. Tight-Binding Picture

4 How Does Electric Current Flow?
4.1 Simplest Model - Drude Theory
4.2 Sommerfeld Theory of Metals.
4.3 Electric Current in Band Picture.

5. Beyond Static Lattice Model. Phonons
5.1 Vibrations of Classical Lattices
5.2 Quantum Mechanics of Lattice Vibrations
5.3 Acoustical and Optical Phonons

II Selected Topics

6. Semiconductors
6.1 Doping. p- and n- Type Semiconductors .
6.2 Heterostructures .
6.3 Devices
6.3. pn Diods
6.3.2 Light Emitting Diods (LEDs)
6.3.3 Transistors

7. Hall Effect

8. Magnetism

9. Superconductivity

Upon successful completion of this course students should be able to:

1. Understand why majority of solids are crystalline.
2. Explore simple solid systems and learn about the temperature and QM effects on crystalline structure and its melting.
3. Hear a review of condensed matter states which are not crystalline like glasses, polymers, liquid crystals and quasi crystals
4. Have an idea of different crystal lattices and their descriptions including notions of classification of Bravais lattices, the notion of reciprocal lattice and the Brillouin zone.
5. Understand the methods one used for the experimental determination of lattice structure with the emphasis on the X-ray diffraction method.
6. Learn of what is the electronic structure of simple crystals, Bloch theorem and electronic bands. On this basis to gain understanding of how and why the realistic materials appear as metals, semiconductors or insulators and how is this related to the original atomic levels.
7. Understand how does electric current flow in crystalline metals, what causes the resistance, what are and what is the role of phonons. |The students will review and further learn about vibrations of classical and quantum lattices and the classification of acoustical and optical phonons.
8. Study a number of selected topics and understand the workings of common semiconductor devices, principles of the magnetism and superconductivity.