The one-particle density matrix $\gamma(x; y)$ is one of the key objects in the quantum-mechanical approximation schemes. The self-adjoint operator $\Gamma$ with the kernel $\gamma(x; y)$ is trace class but a sharp estimate on the decay of its eigenvalues was unknown. In this talk I will present a sharp bound and an asymptotic formula for the eigenvalues of $\Gamma$.

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