One-particle density matrix is the key object in the quantum-mechanical approximation schemes. In this talk I will give a short survey of recent regularity results with emphasis on sharp bounds for the eigenfunctions, and show how these bounds lead to the asymptotic formula for the eigenvalues of the one-particle density matrix. The argument is based on the results of M. Birman and M. Solomyak on spectral asymptotics for pseudo-differential operators with matrix-valued symbols.[-]