Summing over all particles, one finds for Q = ∑ ∑ n X n P n the commutator amounts to i ℏ ℏ [ H , Q ] = 2 T − − ∑ ∑ n X n d V d X n where T = ∑ ∑ n P n 2 2 m is the kinetic energy. The left-hand side of this equation is just ⁠ dQ / dt ⁠, according to the Heisenberg equation of motion. The expectation value ⟨ ⁠ dQ / dt ⁠ ⟩ of this time derivative vanishes in a stationary state, leading to the quantum virial theorem, 2 ⟨ ⟨ T ⟩ ⟩ = ∑ ∑ n ⟨ X n d V d X n ⟩ .