What is the connection between Quantum & Classical Physics? Under what circumstances do the Schrodinger Equation give us the Newton's Laws? This is what we discuss in today's lecture - The Ehrenfest Theorem

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The Ehrenfest theorem relates the average behavior of quantum systems to the classical equations of motion. The theorem states that, on average, the expectation values of quantum mechanical observables follow classical equations of motion. In simpler terms, the Ehrenfest theorem states that the time evolution of the expectation value of momentum is given by the negative of the expectation value of the gradient of the potential.

This lecture requires an understanding of the Schrodinger Equation, and the expectation values of position and momentum.

While quantum mechanics introduces new concepts and behaviors at the microscopic level, the average behavior of a large number of quantum particles tends to resemble classical mechanics. The Ehrenfest theorem provides a formal expression of this connection, emphasizing the transition from quantum to classical behavior in macroscopic systems.

00:00 Introduction
02:46 The Ehrenfest Theorem
20:54 Connection to Newton's Law

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