Schrödinger vs. Heisenberg pictures of quantum mechanics

📚 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:    • The Schrödinger equation  
Time evolution operator:    • The time evolution operator in quantum mec...  
Unitary operators:    • Unitary operators in quantum mechanics  
Expectation values:    • Expectation values in quantum mechanics  
Measurements:    • Measurements in quantum mechanics || Concepts  
The Ehrenfest theorem:    • The Ehrenfest theorem  

⏭️ WHAT NEXT?
Interaction picture: [COMING SOON]

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Director and writer: BM
Producer and designer: MC