Based on the Lindemann criterion one can find an estimate for the critical r s. The criterion states that the crystal melts when the root-mean-square displacement of the electrons ⟨ ⟨ r 2 ⟩ ⟩ is about a quarter of the lattice spacing a. On the assumption that vibrations of the electrons are approximately harmonic, one can use that for a quantum harmonic oscillator the root mean square displacement in the ground state (in 3D) is given by