The Ehrenfest theorem

What is the relation between quantum and classical mechanics?

📚 In this video we explore the time dependence of expectation values of observables in quantum mechanics. When these ideas are applied to the position and momentum of a quantum particle, we end up with Ehrenfest's theorem. This theorem shows that the equations obeyed by the expectation values of position and momentum operators are very similar to the equations of motion of a classical particle. As such, Ehrenfest's theorem allows us to make a connection between the quantum microscopic world and the classical macroscopic world.

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⏮️ BACKGROUND
Schrödinger equation:    • The Schrödinger equation  
Expectation values and root mean square deviations:    • Expectation values in quantum mechanics  
State space and dual space:    • Dirac notation: state space and dual ...  
Hermitian operators:    • Hermitian operators in quantum mechanics  
Commutator algebra:    • Commutator algebra in quantum mechanics  
Functions of operators:    • Functions of operators in quantum mec...  
Wave packets: [COMING SOON]

⏭️ WHAT NEXT?
Constants of motion:    • Constants of motion in quantum mechanics  

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Director and writer: BM
Producer and designer: MC