- #1
rick1138
- 196
- 0
Does anyone know of any tables that show the commutation relations of all QM opeartors? Any information would be appreciated.
You may need a couple more for relativistic quantum physics and spin- Slyboy
Tell that to your friends to impress them.
slyboy said:You don't need a table, they can all be derived simply from
[tex][x,p]=i\hbar[/tex]
You may need a couple more for relativistic quantum physics and spin, but since you didn't specify I am assuming you mean non-relativistic QM.
Yes, and you need the commutators for spin even in nonrelativistic QM, since spin is not derived from x and p.
slyboy said:Yes, but you can derive the relations for orbital angular momentum and they are essentially the same.
Operator commutation relations are mathematical expressions that describe how two operators in quantum mechanics interact with each other. They indicate how the order in which the operators are applied affects the overall result of the operation.
Operator commutation relations are important because they allow us to understand the fundamental principles of quantum mechanics, such as the uncertainty principle. They also play a crucial role in determining the possible states and measurements of quantum systems.
In classical mechanics, the order of operations does not affect the final result. However, in quantum mechanics, the order of operations is crucial and is described by the operator commutation relations. This is due to the probabilistic nature of quantum systems.
Two operators in quantum mechanics are said to commute if their commutator, a mathematical expression that measures the difference between applying the operators in different orders, is equal to zero. This means that the two operators can be applied in any order without affecting the overall result.
Operator commutation relations are used in practical applications of quantum mechanics, such as quantum computing, to determine the possible states and measurements of quantum systems. They also help in the development of new quantum algorithms and technologies.