How does Huang Kun learn solid state physics well? As long as it is a way of thinking.

In Fang Junxin's textbook, briefly (Huang Kun's and keitel's are not very easy to understand, so we should read three books together):

As we know, the crystal is divided into two parts: one is a unit cell that is locally fixed and slightly vibrates in space; The other part is near-free electrons that flow freely in the whole solid space (not free electrons, because the wave functions are different).

For example, crystal is a collective apartment, and one identical house after another is a periodically arranged unit cell; Guests coming and going are all near Free Electronics.

In this case, studying crystals is actually studying two things: periodic cell; Almost free electrons. Then our research is based on this idea.

1. unit cell.

First of all, we should study the periodicity of the unit cell and get the characteristic length of the unit cell. The commonly used technique is X-ray diffraction. This is the first chapter of solid state physics-crystal structure and X-ray diffraction.

The main purpose is to determine how many atoms there are in the unit cell and what is the characteristic length of the unit cell. These two data will be very useful in the future.

Secondly, cells are not static. But in a slight vibration. This vibration is very important for some characteristics of solids: for example, the heat capacity of solids; Solid resistance .......

So how to calculate the heat capacity and resistance of solid by calculating the vibration of unit cell? This is the content of chapter 3-crystal vibration and thermal characteristics of crystal. The decomposition is discussed below;

A: Generally speaking, people are willing to approximate the vibration of cells as intermittent vibration-the treatment method is also very simple. Taylor expansion is carried out in the equilibrium position, ignoring the higher-order term, which is the vibration energy of the internal harmonic oscillator. This technique is very classic, and Rayleigh did the same when calculating the simple harmonic vibration of gas molecules-you must have an idea before doing physics, and don't be in a daze.

B: Well, since the cell is in simple harmonic vibration, let's list a set of equations of simple harmonic vibration, and use lattice characteristic constants here (mentioned in the first chapter, it's very important, isn't it).

Solve this second-order ordinary differential equation, calculate a dispersion relation, and get a linear dispersion relation when the wave vector tends to infinity-by the way, electromagnetic waves will also have dispersion when they pass through the gravitational field. Can you find the characteristics of dispersion equation from these two dispersion relations?

C: By solving the simple harmonic dynamic equation of cells, we can get a continuous solution about the frequency w. However, once we introduce periodic boundary conditions, we find that this solution is quantized.

The quantized frequency w is called phonon.

Phonon is a very important concept to study the internal scattering mechanism of solids. Have a good experience

Phonons are bosons, which obey the Bose distribution. This principle can be used to calculate the heat capacity of solids.

This seems to be a compulsory content.

There is nothing perfect in the world, and imperfection makes things real. So is the crystal. Then the defects inside the crystal are called defects. This study is the fourth chapter-crystal defects and motion.

At this point, the discussion of cell is over. Let's turn to another topic, near-free electrons in crystals.

2. Near-free electrons

We must first know what free electrons are. Free electron is a traveling wave function which is solved with the potential energy term of Schrodinger equation as 0.

So what is a near-free electron? That is, the potential energy term in Schrodinger equation takes the periodic function of cells and the solution is Bloch wave. This is the fifth chapter-solid-state electron theory.

So, don't confuse free electrons with near-free electrons.

Then the energy band can be calculated according to the number of atoms in the unit cell and the characteristic constant of the unit cell (remember, the first chapter has emphasized that it is very important). This is Chapter 6-Energy Band Theory.

One piece of advice for you is to do more exercises. Huang Kun's exercises can be understood by himself after three times.

The video of Jiang Yulong from Shanghai Jiaotong University is very good. You should check it out.