Recent content by AndrewShen

Thanks a lot! Why semiconductor device modelling cannot be solved with ab initio method? What is the difference? You mentioned that tight binding and k.p are empirical or semi-empirical. Is it just because we do not know the exact form of potential? Also, I thought methods like Hartree-Fock...

There are many cases, for simplicity, we choose the wavefunctions to be real. For example, in http://en.wikipedia.org/wiki/Born%E2%80%93Oppenheimer_approximation, there is "The electronic wave functions \chi_k\, will be taken to be real, which is possible when there are no magnetic or spin...

It is very helpful. Still, I have a question. In numerical methods such as OPW and TB, how do we determine the potential V, which is generally unknown. I know there are some empirical methods to determine V, but do we have other choice? Also, it seems that Hartree approximation and...

There are various kinds of approximation methods in band theory. In my opinion, Bloch theorem implies the existence of energy band. From nearly-free electron approximation or tight binding method, we can calculate the energy band. They can tell us the information of band gap and band width...

Orthogonal plane waves can be used to expand Bloch waves. It is better than plane waves because it converges more quickly. However, I've got a problem. The completeness of plane waves is guaranteed by Fourier analysis. Why is OPW complete? It is orthogonal to core levels. But does it mean OPW is...

I am learning Ashcroft's Solid State Physics. In the Electrons in a Weak Periodic Potential, I got some problems. 1. Ashcroft mentioned in the footnote: The reader familiar with stationary perturbation theory may think that if there is no exact degeneracy, we can always make all level...

Thanks! And also thanks to ChrisVer. However, I still don't understand why the representation is essentially irreducible. "A unitary representation is called irreducible if you can reach any normalized state ket of the corresponding space of states by acting with symmetry transformations...

I have several questions about symmetry in quantum mechanics. It is often said that the degeneracy is the dimension of irreducible representation. I can understand that if the Hamiltonian has a symmetric group G, then the state space with the same energy eigenvalue will carry a...