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seen Jul 3 at 13:37

Jun
17
comment Resolution of two frequencies
I still was hoping to have a source for this but I guess that'll do.
Jun
17
comment Resolution of two frequencies
Ok I see. In this case for my purposes I'm considering two identical distributions. If I approximate them as normal distributions then I calculated it means I need a frequency separation of $\Delta\omega > 2\sqrt{\ln (4)}\sigma$
Jun
17
comment Resolution of two frequencies
Sure, I'd be happy to use FWHM, and I understand the subjectivity but there must be a convention that I can implement. My work is theory so I'm not concerned in the details I just want to justify my results and convince others the levels are in principle resolvable. Thank you for the link but this also is talking about angular resolution and I don't see how I can relate it to the question?
Jun
17
asked Resolution of two frequencies
May
11
accepted Derivation of plane wave from inner product of position ket and momentum ket
May
11
accepted Does graphene have a honeycomb lattice?
May
11
accepted Is it physically realistic to have an electric field and polarisation density but no displacement field?
May
11
accepted Multiply creation operator by a phase factor
May
4
asked Multiply creation operator by a phase factor
Apr
25
comment Fourier transform of random variables
Definitely involved, that's why I originally posted as simple a question as I could think to be sign posted along the right path, but there's a lot of reading and searching yet to be done.
Apr
24
comment Derivation of plane wave from inner product of position ket and momentum ket
Thanks for the pointer, I think I've found the relevant material in Sakurai's QM book so I'll check that out.
Apr
24
comment Derivation of plane wave from inner product of position ket and momentum ket
Ok I get this explanation, thanks :)
Apr
24
comment Fourier transform of random variables
Ok maybe I oversimplified the problem. In reality I have a system of interacting nanoparticles described by the non-interacting Hamiltonian shown plus a nearest-neighbour interaction term (described in detail here: arxiv.org/pdf/1411.7796v1.pdf). Basically I just want to know how the game changes when my natural frequency $\omega_0$ can take on a random variable (from a distribution) for each nanoparticle. I want to know how much this disorder smears out the energy spectrum (dispersion) so I know what features will be resolvable.
Apr
24
asked Derivation of plane wave from inner product of position ket and momentum ket
Apr
23
comment Fourier transform of random variables
I edited the question to hopefully make things clearer. Basically I have a real space representation of the Hamiltoniain and I want to go into reciprocal space. I don't know how to treat $\eta$
Apr
23
revised Fourier transform of random variables
added 492 characters in body
Apr
23
comment Fourier transform of random variables
Oh and if people need to choose a distribution to answer the question I would suggest Gaussian, but I don't really mind. To make physical sense it just has to be bunched up around the value $\omega_0$ and die off quickly either side
Apr
23
comment Fourier transform of random variables
Just to be clear I mean that $\omega_0$ changes randomly from each location $\mathbf{R}$ according to some distribution, not that at each location there is some sort of 'blur' of values.
Apr
23
asked Fourier transform of random variables
Apr
7
awarded  Tumbleweed