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The quantum N-body problem is a 3N dimensional problem. If your element has 100 electrons then you need to model a 300 dimensional space. If you took a very coa
by TheEzEzz 15y ago
The quantum N-body problem is a 3N dimensional problem. If your element has 100 electrons then you need to model a 300 dimensional space. If you took a very coarse discretization of 10 cells per dimension, you'd need a computer with at least O(10^300) bits of memory.
- archgoon 15y agoWhich means that you rapidly get into trying to develop a large number of approximation schemes. The validity of each scheme is difficult to determine, and there's always the possibility that the atom, molecule or crystal that you're studying relies upon some feature of the full 300 dimensional picture that you waved away as not being significant. Not only that, but there's a disconnect between what we know about chemistry, and what we know how to interpret from the results of the simulation. Everyone knows that carbon can form 4 bonds, we've known this long before we were sure about electrons. However, trying to explain what this means in terms of electron probability densities is a research problem in itself.
- hammock 15y agoAnd yet we can predict (or at least run a humanly-feasible amount of experiments to discover) the properties of new molecules that are orders of magnitude more complex than an atom, such as recombinant DNA structures and fusion proteins - which are being used to great effect in medicine etc. It blows my mind