Matlab code to calculate silicon band structure using empirical pseudopotential method

This study note and matlab code are totally followed the file from
(1) https://nanohub.org/resources/8405
(2) https://www.ece.nus.edu.sg/stfpage/eleadj/pseudopotential.htm

Also, another great document about this topic can be found at
http://www.scientificpython.net/uploads/1/1/5/9/11598566/epm.pdf

To get the bandstructure start from schrodinger equation


And simplify the Hamiltonian to the following form


Two problem pop up here. How to represent reciprocal lattice vector G and potential V.
For reciprocal lattice vector G, please refer to REF(2).
For potential V, use empirical pseudopotential method and can simplify it to


The final result is not very accurate. Still need works on it.