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  • Constraining densities and potentials

Constraining densities and potentials · Changes

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Update Constraining densities and potentials authored Jan 29, 2025 by Gabriel Wlazłowski's avatar Gabriel Wlazłowski
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Constraining-densities-and-potentials.md
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......@@ -133,7 +133,7 @@ V_{ext}^{(it+1)}(\bm{r}) := V_{ext}^{(it)}(\bm{r}) + ab^{it}\frac{n^{(it)}(\bm{r
```
where $`a,b,c`$ are parameters that need to be adjusted to achieve convergence, $`it`$ stands for the iteration number.
As an example, let us consider the quasi-1D case, where search for the external potential that produces density distribution in the form of two Gaussians:
As an example, let us consider the quasi-1D case, where we search for the external potential that produces density distribution in the form of two Gaussians:
```math
n_0(\bm{r}) = A_1\exp\left(-\frac{(x-x_1)^2}{2\sigma_1^2}\right) + A_2\exp\left(-\frac{(x-x_2)^2}{2\sigma_2^2}\right)
```
......
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