An exception occurs in case when the classical equations of motion are linear, that is, when V is quadratic and V ′ is linear. In that special case, V ′ ( ⟨ X ⟩ ) and ⟨ V ′ ( X ) ⟩ do agree. In particular, for a free particle or a quantum harmonic oscillator, the expected position and expected momentum exactly follows solutions of Newton's equations.