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...
i see... i supposed the SED approach is usually via numerical simulation, so thats why a large scale object like solid state system is too unfriendly..
sorry to intercept.. but..
Do you mean that if i perform a numerical simulation of Maxwell equation on a double slit setup, i will not be able to reproduce the interference effects?
Either u or me are imagining things... but i remember Zapper said it differently. He asked why there's still...
i doubt your question can be tackled using layman understanding, because layman knowledge should only be limited to 3D. :biggrin:
If you want to understand force/dynamics in 4-dimension and its symmetry, you have to just analyse the form of the differential equation. Read something about Lie...
Looks like i got to read a module on superconductor next semester to really appreciate. If you dun mind, pls give me some excellent text books on superconductors.
Also, how QM prediction of simple semiconductor bandstructure and its experimental verification is already phenomenal. There's very remote chance one can reproduce those bunch of curves with one equation :surprised
And the very reason is that QM is inherently a model for describing...
Let me give you a concrete example of a form of highest symmetry ie, a unit radius 'sphere' in n dimensional space. As usual, it is describe by (x1)^2 + (x2)^2 + (x3)^2 + (x4)^2 +(x5)^2 +.... (xn)^2 = 1. Now start with a vector V=(1,0,0,...). Construct any unitary matrix U and act on that V...
Yes. To defy the Bell inquality, we must require the measurement setup to allow the state to project itself into more than one outcome. What i call a one-to-many mapping situation of the local variables. So if we understand the physical mechanism for this process of a state projecting into...
Another curious point. If i want to solve the problem using path integral approach, is it possible? Is tunneling supposed to be described by some instanton equations?
OK. So you are refering to the transmission prob factor in Landaur formalism in conductance calculation. From this point of view, i guess what you posted is reasonable and apparently is the conventional approach to ballistic calculation (except the transmission prob will be described by Airy...
For the Metal-Insulator-Metal case:
How about considering an incident normalised Gaussian wave packet and solve its time dependent Schrodinger solution (assume i can solve it numerically)? The solution will consist of a reflected and transmitted packet. The total prob of transmitted gives...