# Solving many-body problems with a quantum microscope

https://physics.aps.org/synopsis-for/10.1103/PhysRevLett.118.240402

It is known that the Schrödinger equation can not be solved for many body system, but in this article cited above, the wave function for the Bose-Einstein condensate was found experimentally. Does this mean that mathematics is fundamentally limited in describing nature, or that modern mathematics is not sufficiently developed to solve such equations, or that quantum systems are deterministic?

• Yep. In particular, for added explanation, each added particle adds 3 more dimensions to the wave function. And thus if you divide each axis into $N$ "cells" as for a numerical differential equations solver, then there are $N^D$ "hyper voxels" in the wave function input space to sample, where $D$ is the dimension, equal to 3 times the number of particles. This is obviously an exponential function in the dimension $D$ and thus the number of particles. So it is not only NP, it is exponential time AND space. – The_Sympathizer Jun 23 '17 at 4:16
• For example, for 3 particles and 1024 cells, it will take $1024^{3 \cdot 3} = 1024^9$ cells. If you need 8 bytes per cell -- e.g. two single precision IEEE 754 floats, one for the real and one for the imaginary part of the wave function, it will take 8192 Yobibytes to store all this data. For comparison Google's whole server farm is about 13 Exbibytes according to one figure I could dig up provided it was interpreted correctly (and Google keeps the true figure secret so this is a guesstimate), at least as of 2016. So it would take several hundred million Google server farms just to store ... – The_Sympathizer Jun 23 '17 at 4:22