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4h
awarded  Notable Question
Nov
30
comment Hartree-Fock correction to $e$-$e$ interaction
Thanks, could you describe what the graph you sketched in the answer means physically? For $r_s/a_o \approx 4.8 - 12$ we are in the attractive zone of the potential before the repulsion starts at $r_s/a_o < 4.8$?
Nov
30
comment Hartree-Fock correction to $e$-$e$ interaction
Ok thanks, so the additional terms in the so-called correlation energy term are dependant on the free electron energy and give corrections to this. And there are also corrections to the potential energy to account for corrections in the second term. My last question would be are you sure the expansion is valid for $r_s \ll 1$? I checked AAM and my notes and they both say $r_s/a_o \ll 1$, which is why I was confused about the applicability of this expansion to metals given the typical range of $r_s/a_o$ for them
Nov
30
comment Hartree-Fock correction to $e$-$e$ interaction
I see, so is there any way to argue that there must be kinetic energy terms in these additional terms?
Nov
30
comment Hartree-Fock correction to $e$-$e$ interaction
Also given that the pertubative expansion is only valid for $r_s/a_o \ll 1$, and most metals have this ratio in the range $2-6$ this means higher order corrections are important in this expansion. For sodium for example $r_s/a_o \approx 4$ which is close to the minimum you mentioned. So this means this value lies in the repulsive end of the graph you drawn and hence the expansion is not valid?
Nov
30
comment Hartree-Fock correction to $e$-$e$ interaction
Hmm, my question on my sheet is 'The subsequent terms $0.0622 \ln (r_s/a_o) -0.096 + O(r_s/a_0)$' are collectively known as the correlation energy. Explain why these contain contributions from the kinetic energy as well as the potential energy'?
Nov
30
comment Hartree-Fock correction to $e$-$e$ interaction
Thanks for the edits. But how is $\mathcal V$ explicitly got terms in kinetic energy? As far as I can see, there are only contributions from the positive ionic background, electron-ion interaction and electron-electron interaction which all contribute to the potential energy just?
Nov
29
comment Hartree-Fock correction to $e$-$e$ interaction
Many thanks for your answer. I have not studied the Hartree-approximation using your method of annihilation operators so I could not follow your mathematics exactly. (I am following the method in Ashcroft and Mermin (AAM)). I could not understand the part where you say the second term of $\mathcal H$ is the result of mixing of the subsequent terms. Could you maybe describe this part in words or at the level of the notation of AAM? I think the method of AAM is the same you used, just not in the operator formulism. Thanks
Nov
29
asked Hartree-Fock correction to $e$-$e$ interaction
Oct
24
asked Relaxation time approximation in Drude model apparant paradox
Oct
17
asked Resources to learn about the Higgs theory at undergraduate level
Sep
22
comment Packing fraction of atoms in a HCP structure
Hi Jon. Could you elaborate on the geometry? It is probably simple, but I have stared at it for some time and can't get it right. Thanks.
Sep
22
comment Packing fraction of atoms in a HCP structure
yes, that is what I assumed. For some reason, the geometry I can't get quite right.
Sep
22
comment Packing fraction of atoms in a HCP structure
ah cool thanks ;) Yes, it is their $c$ that I am struggling to derive. Do you have any pointers?
Sep
22
asked Packing fraction of atoms in a HCP structure
Sep
18
comment Question about derivation of tensor in Di Francesco's CFT
For clarity, it was uncovered that there is indeed no trace anomaly and that the vanishing of the trace still holds everywhere even when we include the addition of $A_5$. This may be the reason why the author neglected its addition, viewing it as perhaps a superfluous term or maybe there is more to it.... So the question is still open for answers to anybody else who is interested. Thanks.
Sep
16
comment Question about derivation of tensor in Di Francesco's CFT
Hi Dilaton, thanks for commenting here, I do not remember posting my question on overflow. I could not understand the argument very well, what does it mean to say a 'trace anomaly'?
Sep
13
comment Demostrating possible equivalence of two tensors
I made another thread, but it doesn't seem to be attracting a lot of attention. Do you think it would be okay to contact the author about this?
Sep
13
accepted Demostrating possible equivalence of two tensors
Sep
12
asked Question about derivation of tensor in Di Francesco's CFT