I am looking for a way to connect the Condon-Shortley-Wigner to the Edmonds phase convention. Specifically I am writing a program to compute Wigner-d matrix coefficients
From tabulated values (e.g. even Wikipedia) d^1/2_{1/2,-1/2}=(-1)^{-1/2-1/2}d^1/2_{-1/2,1/2}=-sin(theta/2)
So...
Homework Statement
Suppose we can calculate a quantity f(t) and we need its Fourier transform F(w). Looks to me that accuracywise Filon's rule, e.g. approximating the computed f(t) by splines and analytically integrating piecewise should be more accurate than an FFT, at least for a smooth...
Because the mobile plasma charges(i.e. electrons first) will rearrange themselves because of the field, so as to resist it. But if the field changes sign before the electrons can move, they are 'confused', i.e. they start moving one way to resist the field, but the field sign changes sign before...
If you have a problem with spin, try some more exotic notion such as charm.
It was Feynman who said that if we cannot explain something in simple terms, it means we do not understand it well. And yes, Feynman also said "nobody understands quantum mechanics" and this is normal, because our...
Another question on decoherence: Take stat mechanics. There we have an atomic system and an environment(consisting of atomic subsystems that will be traced over) plus an interaction between them, V(t). The atomic system could be for example an atom and the environment could reprsent collisions...
No, in both cases you detect N1+N2, but that is if you have one HUGE detector that will grab anything past the slits, or alternatively a large number of detectors that cover all space past the slits. The interference pattern has to do with the distribution of photons caught by each such...
Look in my example for Ly-a: Assuming a diagonal density matrix,
the Trace is
sum_m <21m|rho|21m><21m|d|100><100|d(t)|21m>
no parity issue here.
The relative contribution to any particular line is proportional to the upper level population,
which (for a diagonal density matrix) is...
d is dipole moment. rho is the density matrix. Why is d constant? You need matrix elements of d to do the trace. You can get a constant reduced matrix element out of d, but you still have the Clebsch-Gordan to sum
e.g. Ly-a:(sum over m)
<100|d|21m><21m|d(t)|100>
I don't think that's right. Coulomb waves have the correct asymptotic behavior, but the point is that this is merely a basis; you can use any basis you want to represent the states and clearly bound states +say Coulomb waves is a complete basis. What's the point of non-stationary autoionizing...
Actually when you diagonalize you solve the problem EXACTLY to all orders(in the framework of the set of states you use). It's when you have both degenerate and nondegenerate that order makes sense. To your question, if in the degerenate subspace the perturbation is 0, then to get a nonzero...
In terms of stationary states we have bound states and free(plane wave or Coulomb) states
Autoionizing states are free(E>0), e.g. continuum, but localized states(resonances). Hence
wavepackets consisting of a band of plane or Coulomb waves. I understand they may be long-lived, longer than the...
If any experiment can only give a single result, then there is no uncertainity.
In this case where we start with a prepared state |1>, a measurement of O2 can only give the result |2>. It has 100% |2> character and 0% |1> character.
In contrast if O2|1> were a|1>+b|2>, then the outcome would...