Ehrenfest Theorem

Quantum expectation values obey classical equations of motion, bridging quantum and classical mechanics.

Core Principles & Analysis

• Derived by Paul Ehrenfest in 1927.
• Shows that quantum expectation values of position and momentum obey Newton's second law on average.
• Reproduces classical trajectories exactly for potentials up to quadratic order, such as the harmonic oscillator.

Specifications & Metrics

• SYMBOL: d⟨p⟩/dt = -⟨∇V⟩