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  1. Q

    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. Q

    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. Q

    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. Q

    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. Q

    Atomic spectra evidence for relativistic potential

    just bumping it up to see if someone can help..
  6. Q

    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. Q

    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.
  8. Q

    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...
  9. Q

    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...
  10. Q

    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.
  11. Q

    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}
  12. Q

    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...
  13. Q

    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...
  14. Q

    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?
  15. Q

    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] ?
  16. Q

    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..
  17. Q

    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...
  18. Q

    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!
  19. Q

    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:
  20. Q

    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...
  21. Q

    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.
  22. Q

    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...
  23. Q

    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...
  24. Q

    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...
  25. Q

    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?
  26. Q

    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...
  27. Q

    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.
  28. Q

    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...
  29. Q

    Exact calculation of tunneling current?

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