**EE123 A, Fundamentals of Solid-State I, Fall 2016, UCLA **

Instructor: Professor Marko Sokolich

Teaching assistant: Qiming Shao

Discussion section: 9:00 -9:50 am Monday, BOELTER 5419

Office hours: 10 - 11 am Monday, 3 - 4 pm Tuesday, TA room at Engineering IV 6th floor

**Week #1 discussion section notes**

In this week, we are going to review the application of time-independent Schrödinger equation in solving the single particle in an infinite square well problem. Then, we will try to qualitatively understand what will happen when the well is not infinite. We also qualitative treat the case of a particle in two closely spaced finite wells. This section will be a good introduction for the covalent bonding (e.g., electron in H+ molecules) in the following lectures.

Key points: time-independent Schrödinger equation, separation of variables, normalization, continuity boundary conditions, odd and even functions

References: [1] https://en.wikipedia.org/wiki/Finite_potential_well

[2] David Griffiths, introduction to quantum mechanics, second edition, chapter two

**Week #2 discussion section notes **(see attachment)

Two closely spaced finite square potential wells and its analogy to the electron in H+ molecule;

Reciprocal space and lattice vector;

Bragg's law and diffraction conditions

**Week #3 discussion section notes**

Phonon dispersion of one-dimensional (single) atom chain

Long-wavelength limit; Brillouin zone; group velocity

**Week #4 discussion section notes **(see attachment)

Phonon dispersion of diatomic linear lattice with mass M1 and M2 (M1>M2)

Quantization of elastic waves - phonon

**Week #5 discussion section notes**

Introduce my approach to solving any homework problem (see attachment)

Homework problems: 1. phonon dispersion of monoatomic linear lattice with different force constants

2. density of states in 3D, 2D and 1D

3. why metals do not form simple cubic structure

**week #6 (no discussion section since I am out of town for MMM conference)**

**Week #7 discussion section notes**

Review of midterm questions

One important question is to know how to use three types of distribution functions: Maxwell-Boltzmann, Fermi-Dirac, Bose-Einstein

**Week #8 discussion section notes**

Kronig-Penney model

**Week #9 discussion section notes**

Central equation, k-space of Schrödinger equation, and its three applications

Empty lattice approximation (free electron model), band gap at the boundary of first Brillouin zone, energy bands near the boundary

**week #10 discussion section notes**

Application of central equation for empty lattice approximation, that is, calculation of energy bands along [111] for fcc crystal structure

Two-dimensional maximum surface resistance (discussed in the office hour)

Attachments