# Recent content by QMrocks

1. ### Addition Theorem for Spherical Harmonics

i uploaded the pdf for you (i reprint it 2 pg in 1 to meet the size limit here).
2. ### Addition Theorem for Spherical Harmonics

thanks all! It will take me some to digest these info. i hope i can arrive at a close form for my question. my only basis for believing so is that the spherical harmonics of order L is a complete basis for any polynomial function of order L, hence it should be able to describe the spherical...
3. ### Addition Theorem for Spherical Harmonics

Happy New Year all!! i have a question regarding the addition theorem for spherical harmonics. In JD Jackson book pg 110 for e.g. the addition theorem is given as: P_{L}(cos(\gamma))=\frac{4\pi}{2L+1}\sum_{m=-L}^{L}Y^{*}_{Lm}(\theta',\phi')Y_{Lm}(\theta,\phi) where...
4. ### Atomic spectra evidence for relativistic potential

Thanks Zapper. i tried to search the internet abt that. But i retrieve bunch of results not really pertaining to what i want. Just wondering if that 3rd term in the equation has a name? i search for 'relativistic correction to potential energy' and it does not help...
5. ### Atomic spectra evidence for relativistic potential

just bumping it up to see if someone can help..
6. ### Atomic spectra evidence for relativistic potential

In L. I. Schiff book, one can follow his derivation of the Hamiltonian from Dirac relativistic equation and obtain the following.. \left[\frac{\vec{p}^2}{2m}+V-\frac{\hbar^2}{4m^{2}c^{2}}\frac{dV}{dr}\frac{\partial}{\partial r}+\frac{1}{2m^{2}c^{2}}\frac{1}{r}\frac{dV}{dr}\vec{S}\cdot...
7. ### Spin Orbit Interaction Hamiltonian

if we began from Dirac equation, we can obtain the Hamiltonian just like the form in Jackson book. i find L. I. Schiff's book extremely well explained.

Thank you!
9. ### Spin Orbit Interaction Hamiltonian

Spin Orbit Interaction Hamiltonian is defined as follows: H_{SO}=\frac{1}{2m_{e}c^2}\frac{1}{r} \left(\frac{\partial V}{\partial r}\right)L\cdot S How does one derive the above Spin Orbit Interaction Hamiltonian from relativistic treatment? Is there a good textbook that elaborates on...
10. ### Valley degeneracy

There are only degeneracy for indirect semicon because the conduction valley minima can be allowed to have minima in k-space which are symmetrically the same. Direct bandgap means the minima is at [0,0,0] and there is no other accompanied valley minima. Except for the case of valence band...
11. ### Valley degeneracy

just consider the case of bulk onductor like Si. The valley minima along delta direction which in the momentum space is denoted by the direction vector [0,0,1] [0,1,0] etc. There are six such possible direction, resulting in a valley degeneracy of six.
12. ### What function correspond to this series expansion?

Anyone knows what function correspond to this series expansion? \begin{align} f(x)=1+x+x^2+x^3+... \end{align}