Recent content by QMrocks

  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...
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    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.
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    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?
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