Classical equations from Ehrenfest theorem

For

H = p^{2} / (2 m) + U (x)

m \frac{d}{d t} ⟨ x ⟩ = ⟨ p ⟩, \frac{d}{d t} ⟨ p ⟩ = - ⟨ U^{'} (x)⟩, \frac{d}{d t} ⟨ H ⟩ = 0.

These are the expectation-value analogues of Newton's second law and conservation of energy.

 Ancestors (5)