Why we cannot solve many-body Schrodinger equation like this in finite different method?

Question

why we cannot solve many body Schrodinger equation like this in finite different method? Could you give me some details?

Answer 1

You can. But Schrödinger's equation is an equation in configuration space, which means that you will have $3n$ dimensions for $n$ particles, and most of that will be useless space. If you split each dimension into $N$ equal widths, then you will have to keep track of $N^{3n}$ positions. For all but the smallest systems, this is just too much computational time and storage usage.