Comment on How probable is Molecular Nanotech?

Sat, 29 Jun 2013 17:33:14 GMT

I was specifically referring to the difficulty of solving it for determining electron position, which, in the classical limit is exactly analogous to infinitesimal points moving around based on forces that obey an inverse square law.

I thought you were talking about quantum difficulties in arranging on the nano scale? I am not sure what your classical limit is, but I am not sure it would apply to the argument you originally made.

The Hamiltonians for the 2 systems are essentially identical. If you treat electrons as having a well-defined position and momentum (hence the classical limit) then the problem of atomic bonding is exactly the same as the gravitational n-body problem (plus a sign change to handle repulsion). I'll have to sit down and do a bunch of math before I can say how exactly the quantum aspects affect the infinite series solution presented. But my general statement that

is trivially true, and this is why I introduced solving the many-body S.E. as approximately equivalent to the n-body problem.

To pick an obvious observation: if we have an exact solution, however inefficient, does that not immediately give us both theoretical and empirical ways to justify the fast approximations by comparing them to the exact answers using only large amounts of computing power - and never appealing to experiments?

Exactly why I think you've made a good point. I need to look at the approximation and see if it's possible. If it has 10^24 derivatives to get chemical accuracy, and scales poorly with respect to n, then it's probably not useful in practice, but the argument you make here explicitly is exactly the argument I understood implicitly from your previous post.

Discuss