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Solid state frens, help pls

Anonymous Sun 21 Mar 08:07:21 2021 No.12862051 View Reply Original Report

Quoted By: >>12862066 >>12862182

Why is
$\sum_{n}^{N}e^{i\left(\vec{q}+\vec{k}_i-\vec{k}_f\right)\vec{R}_{n}}=N^3\delta_{\vec{q}+ \vec{k}_i, \vec{k}_f}<script type="math/tex"> sum goes over all unit cells of a crystal.$

Anonymous

Anonymous Sun 21 Mar 2021 08:15:23 No.12862066 Report

Quoted By:

>>12862051
$\sum_{n}^{N}e^{i \left( \vec{q}+\vec{k}_i- \vec{k}_f \right) \vec{R}_{n}}=N^3 \delta_{ \vec{q}+ \vec{k}_i, \vec{k}_f}$

Anonymous

Anonymous Sun 21 Mar 2021 08:16:54 No.12862070 Report

Quoted By:

$\sum_{n}^{N}e^{i \left( \vec{q}+ \vec{k}_i- \vec{k}_f \right) \vec{R}_{n}}=N^3 \delta_{ \vec{q}+ \vec{k}_i, \vec{k}_f}$

Anonymous

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Anonymous Sun 21 Mar 2021 08:18:11 No.12862072 Report

Quoted By: >>12862165 >>12862182

Anonymous

Anonymous Sun 21 Mar 2021 08:20:05 No.12862074 Report

Quoted By:

$ \sum_{n}^{N}e^{i \left( \vec{q}+ \vec{k}_i- \vec{k}_f \right) \vec{R}_{n}}=N^3 \delta_{ \vec{q}+ \vec{k}_i, \vec{k}_f} $

Anonymous

Anonymous Sun 21 Mar 2021 08:21:31 No.12862076 Report

Quoted By:

$\displaystyle \sum_{n}^{N}e^{i \left( \vec{q}+ \vec{k}_i- \vec{k}_f \right) \vec{R}_{n}}=N^3 \delta_{ \vec{q}+ \vec{k}_i, \vec{k}_f} $

Anonymous

Anonymous Sun 21 Mar 2021 08:27:34 No.12862091 Report

Quoted By:

>Vectors as exponents
I'm out, good luck

Anonymous

Anonymous Sun 21 Mar 2021 09:09:06 No.12862165 Report

Quoted By: >>12862182

>>12862072
As far as i remember you can turn that sum into integral with some prefactor, (maybe N/(2pi)^3 or something similar). When you do that and you use the definition of discreete delta funciton you should get the conservation of momentum and some factor that should all turn out to N^3

Anonymous

Anonymous Sun 21 Mar 2021 09:20:14 No.12862182 Report

Quoted By:

>>12862165
>>12862072
>>12862051
You don't even need to approximate it by an integral. Just use the geometric sum formula. (I assume there should be a dot product in between the parentheses and R.)

Anonymous

Anonymous Sun 21 Mar 2021 09:33:43 No.12862211 Report

Quoted By:

yo I'm a chemist what's all this for? crystal lattice energy or similar? seems indarasting

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