# Units

we work in a natural unit-system where $\hbar = m = 1$ (m is the mass of $^{87} Rb$). This simplifies the Schröedinger-equation to:

$i \frac{\partial\Psi}{\partial t} = -\frac{1}{2} \frac{\partial^2 \Psi}{\partial x^2} + V(x,t) \Psi$

This means that any value output from the Composer will have to be multiplied by the following numbers to get a value in SI-units:

space: $532 nm$

energy: $2.722791 \cdot 10^{-31} J$, $1.699432 \cdot 10^{-12} eV$

time: $0.3873128 ms$

Natural units are used so the scale of the actual number being used by the computer are close to 1. Too small numbers would impede accuracy of the simulation. The exact choice of unit system is based historically in the fact that the research group behind ScienceAtHome and Quatomic works with Rubidium-87 atoms in optical lattices using a $1064 nm$ laser, which has a lattice-spacing of $\lambda/2 = 532 nm$.