Eigenvalue asymptotics for the one-particle density matrix

Abstract: The one-particle density matrix

g a m m a (x, y)

for a bound state of an atom or molecule is one of the key objects in the quantum-mechanical approximation schemes. We prove the asymptotic formula

l a m b d a_{k} s i m (A k)^{- 8 / 3}

,

A g e 0

, as

k o i n f t y

, for the eigenvalues

l a m b d a_{k}

of the self-adjoint operator

with kernel

g a m m a (x, y)

.

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