Quantum Chemistry 4.6 – Commutators

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.

Notes Slide: http://i.imgur.com/0fKXddU.png

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