Eigenvalue asymptotics for the one-particle density matrix
Eigenvalue asymptotics for the one-particle density matrix
The one-particle density matrix γ(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 λk∼(Ak)−8∕3, A≥0, as k→∞, for the eigenvalues λk of the self-adjoint operator Γ≥0 with kernel γ(x,y).