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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}
13. Determinants and Adjoints

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...
14. Would forces act with the same symmetry in 4D as it does in 3D?

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...
15. Revival of CM ?

So are you saying that EM theory is not part of CM? And SED has an alternative version of EM theory that does not invoke the idea of superposition?
16. A trick to solve functional integraltion?

LHS is a path integration over \phi. How did you drop that path on RHS i.e. \int{d[\phi] ?
17. Revival of CM ?

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..
18. Revival of CM ?

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...
19. Revival of CM ?

Great! i love Dover books (and i happen to have Michael Tinkham's Group theory book too). Will check out on these two books. Thanks for the tip again!
20. Would forces act with the same symmetry in 4D as it does in 3D?

Trueness. 'Be patient' thats what my QM teacher always say. :tongue:
21. Would forces act with the same symmetry in 4D as it does in 3D?

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...
22. Revival of CM ?

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.
23. Revival of CM ?

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...
24. Would forces act with the same symmetry in 4D as it does in 3D?

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...
25. Proof of non-locality indep. of conservation law

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...
26. Exact calculation of tunneling current?

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?
27. Exact calculation of tunneling current?

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...
28. Proof of non-locality indep. of conservation law

OK. Thanks for the tips. BTW, i love Dover books. That definitely looks like one i should have in my collection too.
29. Exact calculation of tunneling current?

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...
30. Exact calculation of tunneling current?

May i know based on what argument you can associate the tunneling conductance with that exponential?