Professor M does Science | The Ehrenfest theorem @ProfessorMdoesScience | Uploaded June 2021 | Updated October 2024, 1 hour ago.
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: youtu.be/CKpx9hkQ3HM
Expectation values and root mean square deviations: youtu.be/rEm-Ejg5xek
State space and dual space: youtu.be/hJoWM9jf0gU
Hermitian operators: youtu.be/XIgDUfyrLAY
Commutator algebra: youtu.be/57xgSIV9PY0
Functions of operators: youtu.be/nqLEbrzVsk4
Wave packets: [COMING SOON]

⏭️ WHAT NEXT?
Constants of motion: youtu.be/r38VW3JwBAk

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Director and writer: BM
Producer and designer: MC