Types-of-codes.md

+# Static and time-dependent codes
+There are two main branches of codes:
+* Static codes `st-wslda-?d` for solving self-consistently static DFT equations
+* Time-dependent codes `td-wslda-?d` for solving time dependent DFT equations. The `td-wslda-?d` codes require starting point for the time evolution (i.e $`\psi(\vec{r},t=0)`$) which is typically generated by the static codes.
+
+
+### Codes dimensionality
+#### 3D codes
+The 3D codes do not impose any restriction for form of the wave-functions. The wave-functions are assumed to be:  
+![\psi=\varphi(x,y,z)](https://render.githubusercontent.com/render/math?math=%5Cpsi%3D%5Cvarphi(x%2Cy%2Cz))
+
+#### 2D codes
+In 2D codes the wave-functions are assumed to be:  
+![\psi=\varphi(x,y)\frac{1}{\sqrt{L_z}}e^{ik_z z}](https://render.githubusercontent.com/render/math?math=%5Cpsi%3D%5Cvarphi(x%2Cy)%5Cfrac%7B1%7D%7B%5Csqrt%7BL_z%7D%7De%5E%7Bik_z%20z%7D%0A)  
+where  
+![k_z = 0, \pm 1 \frac{2\pi}{L_z}, \pm 2 \frac{2\pi}{L_z}, \ldots , +(N_z-1) \frac{2\pi}{L_z}](https://render.githubusercontent.com/render/math?math=k_z%20%3D%200%2C%20%5Cpm%201%20%5Cfrac%7B2%5Cpi%7D%7BL_z%7D%2C%20%5Cpm%202%20%5Cfrac%7B2%5Cpi%7D%7BL_z%7D%2C%20%5Cldots%20%2C%20%2B(N_z-1)%20%5Cfrac%7B2%5Cpi%7D%7BL_z%7D%0A)  
+For `NZ=1` the code solves 2D problem (there is only one mode in z-directions, which reduces to 1). Note however, that 2D problem requires different prescription for coupling constant regularization than the one implemented in w-SLDA toolkit. 
+
+
+#### 1D codes
+In 1D codes the wave-functions are assumed to be:  
+![\psi=\varphi(x)\frac{1}{\sqrt{L_y}}e^{ik_y y}\frac{1}{\sqrt{L_z}}e^{ik_z z}](https://render.githubusercontent.com/render/math?math=%5Cpsi%3D%5Cvarphi(x)%5Cfrac%7B1%7D%7B%5Csqrt%7BL_y%7D%7De%5E%7Bik_y%20y%7D%5Cfrac%7B1%7D%7B%5Csqrt%7BL_z%7D%7De%5E%7Bik_z%20z%7D%0A)  
+where  
+![k_y = 0, \pm 1 \frac{2\pi}{L_y}, \pm 2 \frac{2\pi}{L_y}, \ldots , +(N_y-1) \frac{2\pi}{L_y}](https://render.githubusercontent.com/render/math?math=k_y%20%3D%200%2C%20%5Cpm%201%20%5Cfrac%7B2%5Cpi%7D%7BL_y%7D%2C%20%5Cpm%202%20%5Cfrac%7B2%5Cpi%7D%7BL_y%7D%2C%20%5Cldots%20%2C%20%2B(N_y-1)%20%5Cfrac%7B2%5Cpi%7D%7BL_y%7D%0A)  
+![k_z = 0, \pm 1 \frac{2\pi}{L_z}, \pm 2 \frac{2\pi}{L_z}, \ldots , +(N_z-1) \frac{2\pi}{L_z}](https://render.githubusercontent.com/render/math?math=k_z%20%3D%200%2C%20%5Cpm%201%20%5Cfrac%7B2%5Cpi%7D%7BL_z%7D%2C%20%5Cpm%202%20%5Cfrac%7B2%5Cpi%7D%7BL_z%7D%2C%20%5Cldots%20%2C%20%2B(N_z-1)%20%5Cfrac%7B2%5Cpi%7D%7BL_z%7D%0A)  
+For `NY=1` and `NZ=1` the code solves 1D problem . Note however, that 1D problem requires different prescription for coupling constant regularization than the one implemented in w-SLDA toolkit. 
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