Professor M does Science | Schrödinger vs. Heisenberg pictures of quantum mechanics @ProfessorMdoesScience | Uploaded April 2022 | Updated October 2024, 1 hour ago.
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📚 Time evolution in quantum mechanics can be described in various alternative but equivalent ways, each of which referred to as a "picture". We can relate the different pictures by unitary transformations driven by time evolution operators. In this video, we compare two of the most common pictures, the Schrödinger picture and the Heisenberg picture. In the Schrödinger picture, time evolution is encoded by states, while in the Heisenberg picture states are time independent and the time evolution is encoded by the observables.

0:00 Intro
0:52 Schrodinger picture
4:52 Time evolution operator
6:54 Heisenberg picture - simple motivation
11:08 Unitary transformations
13:32 Pictures of time evolution in quantum mechanics
16:28 Heisenberg picture
22:52 Dynamics
27:31 Conservative systems
30:14 Why use the Heisenberg picture?
32:42 Wrap-up

⏮️ BACKGROUND
Schrödinger equation: youtu.be/CKpx9hkQ3HM
Time evolution operator: youtu.be/zqmU4dW03aM
Unitary operators: youtu.be/baIT6HaaYuQ
Expectation values: youtu.be/rEm-Ejg5xek
Measurements: youtu.be/u1R3kRWh1ek
The Ehrenfest theorem: youtu.be/55RQCCtdlko

⏭️ WHAT NEXT?
Interaction picture: [COMING SOON]

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Director and writer: BM
Producer and designer: MC