 Paul Ehrenfest

Paul Ehrenfest connected quantum expectation values with classical-looking equations of motion. For suitable quantum states evolving under the Hamiltonian $H=p^2/(2m)+V(x)$, the Ehrenfest theorem gives $d⟨x⟩/dt=⟨p⟩/m$ and $d⟨p⟩/dt=-⟨V^{\prime }(x)⟩$. Here $V$ is potential energy. The mean force need not equal the force evaluated at the mean position. If $V$ is a quadratic function, it does; for more general potential energy functions, a sufficiently narrow wave packet can justify an approximation. The theorem therefore states precisely which comparison between quantum mechanics and classical mechanics is exact and which step needs another assumption.^[ref]

A physicist associated with the Ehrenfest theorem and, with Tatyana Afanasyeva-Ehrenfest, the Ehrenfest model.

Paul Ehrenfest was an Austrian physicist born on January 18, 1880, and he passed away on September 2, 1933. He is known primarily for his contributions to statistical mechanics, thermodynamics, and the foundations of quantum theory. Ehrenfest developed important concepts in these fields, including the Ehrenfest theorem, which relates the time evolution of quantum mechanical observables to classical mechanics.