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...
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...
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...
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...
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.
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...
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...
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.
how many definitions does adjoint take?
1) there is the classical adjoint (its exact definition too messy to write) which has the useful relation A^(-1)=Adj(A)/det(A).
2) then there is the definition of adjoint as the transpose and conjugate of a matrix.
These two adjoint operation are...
And if Feynman could not reduce it, not many in this world can do it then. :tongue: But what you said is right. True understanding entails the ability to reduce the problem to something simple. My QM lecturer did just that. He reduce QM formalisms to just a pair of non-commuting unitary...