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Quantum Chemistry 4.6 - Commutators
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Short lecture on operator commutators in quantum mechanics.
The commutator of two operators A and B is the difference between acting on a wavefunction with B then A and A then B. Operators act on a function from right to left. If the commutator of two operators is zero, then A and B are said to "commute". If A and B do not commute, then "uncertainty" exists between the measuring of physical properties A and B. There is an inverse relationship between the uncertainty in one property and the uncertainty in the other. The magnitude of the uncertainty is determined by the Schrodinger-Robertson uncertainty relationship. From this, we can derive the Heisenberg uncertainty principle for position and momentum.
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All TMP Chem content is free for everyone, everywhere, and created independently by Trent Parker.
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The commutator of two operators A and B is the difference between acting on a wavefunction with B then A and A then B. Operators act on a function from right to left. If the commutator of two operators is zero, then A and B are said to "commute". If A and B do not commute, then "uncertainty" exists between the measuring of physical properties A and B. There is an inverse relationship between the uncertainty in one property and the uncertainty in the other. The magnitude of the uncertainty is determined by the Schrodinger-Robertson uncertainty relationship. From this, we can derive the Heisenberg uncertainty principle for position and momentum.
--- About TMP Chem ---
All TMP Chem content is free for everyone, everywhere, and created independently by Trent Parker.
--- Video Links ---
--- Social Links ---
--- Equipment ---
Microphone: Blue Yeti USB Microphone
Drawing Tablet: Wacom Intuos Pen and Touch Small
Drawing Program: Autodesk Sketchbook Express
Screen Capture: Corel Visual Studio Pro X8
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