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Is the quantum $n$-body problem as difficult as the classical $n$-body problem?

Or quantum mechanics allows to get a simpler exact solution?

Suppose there are 3 particles with uniform potential field. Can their wave functions be found exactly?

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Have a look of how quantum mechanics solves the many body problem en.wikipedia.org/wiki/Many-body_problem –  anna v Sep 21 '12 at 15:37
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@annav: The wikipedia page is not very informative. –  Arnold Neumaier Sep 21 '12 at 15:40
    
Related classical problem: physics.stackexchange.com/q/1235/2451 –  Qmechanic Jun 6 '13 at 15:20
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up vote 4 down vote accepted

The quantum $n$-body problem is considerably simpler than the classical $n$-body problem, since the problems with collisions disappear. Rigorous existence results are much stronger. See, e.g., the book ''Scattering theory of classical and quantum N-particle systems'' by Derezinski and Gérard.

But explicit solutions are about as rare in the quantum case as in the classical case.

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