Linear combination of atomic orbitals (tight-binding method) for electrons in crystalline solids

[@ankidokolo]

Thank you Sir for the great series. I have just one comment. When you are discussing the orthogonality for the second configuration, where atoms are close to each other, you are using the expression "not valid". These ARE valid, since, using the matrix form of the eigenvalue problem, we can write : Hc=ESc where S is the overlap matrix. We can show that we can enforce S to be the identity matrix, and we can therefore use those Bloch's wavefunctions that we got for the first configuration. This way, we don't need the orthogonalizing precedur that you went through at the end of the video.

[@SampleroftheMultiverse]

For those That prefer a mechanical analog you can look at harmonics of a guitar string and such. The video I present is another mechanical method of quantizing a system. It is one of two methods where structures can actually be produced. kzbin.info/www/bejne/raOlpKSfepWpfZYsi=waT8lY2iX-wJdjO3 Area under a curve is often equivalent to energy. Buckling of an otherwise flat field shows a very rapid growth of this area. If my model applies, it may show how the universe’s energy naturally developed from the inherent behavior of fields. Under the right conditions, the quantization of a field is easily produced. The ground state energy is induced via Euler’s contain column analysis. Containing the column must come in to play before over buckling, or the effect will not work. The sheet of elastic material “system” response in a quantized manor when force is applied in the perpendicular direction. Bonding at the points of highest probabilities and maximum duration( ie peeks and troughs) of the fields “sheet” produced a stable structure when the undulations are bonded to a flat sheet that is placed above and below the core material.

[@SampleroftheMultiverse]

12:36

[@没有巅峰人生永远是上]

does the orthogonalizing process appllied to the calculaiton of bandstructure of the graphene in the later slides? If yes, how to do this there? Thanks