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  1. 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...
  2. 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...
  3. 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...
  4. 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}
  5. Q

    Exact calculation of tunneling current?

    Supposed we have a metal sandwitched between two thin dielectrics. If i contact an electrical voltage on the dielectric, there will be tunneling current due to electron tunneling from the metal across the dielectric. i could attempt to calculate this current from a semiclassical approach using...
  6. Q

    Proof of non-locality indep. of conservation law

    EPR argument makes use of conservation of momentum between two outgoing particles. Einstein boxes argument makes use of conservation of particle numbers. Anybody can tell me an experiment which proves that QM is non-local without invoking conservation law?
  7. Q

    Rotational Raman Spectra

    Hi all, i am studying the physics of Raman Spectra. Was able to understand the origin of Vibrational Raman Spectra... which was an effect due to the change of polarizability with internuclear distance due to molecular vibration. But, i still yet to figure out why rotation of molecules can...
  8. Q

    Quaternion and Pauli matrix

    i am learning Quaternion now for my EM course. Can someone enlighten me on the correspondence between Quaternion and Pauli Matrix algebra?
  9. Q

    QM and Sturm Liouville Theory

    Can someone pls explain what is the significance of Sturm Liouville Theory to Quantum Mechanics?
  10. Q

    Do you know what this particular unitary operator is?

    Recall that the unitary operator exp(\frac{i}{\hbar}aX) transform the operator P_x +a to P_x . Now, what is the unitary operator that transform the operator P_x +aX to P_x ?? :confused:
  11. Q

    Advanced and retarded Green's function

    anybody can recommend a good introducotry book on "advanced and retarded Green's function" and its application to QM, particularly transport problems. Thanks. :smile: