What Are Commutators and Their Role in Quantum Mechanics?

In summary, the conversation is about commutators in quantum mechanics. The person asking for help has missed classes and is looking for information on what a commutator is and its role in quantum mechanics. They also mention previous knowledge of momentum and energy operators and ask for study materials online. Some sources are suggested and the person is advised to formulate specific questions for better responses. The person apologizes for previous outbursts and thanks others for their responses.
  • #1
schumi1991`
30
0
Commutators In quantum...!

Recently my class was taught about commutators and their applications in angular momentum operator.Unfortunately due to health reasons I was not able to attend them and now can't get any extra classes and to make things worse the books I was consulting don't have this topic altogether.
I would really like to ask as to what is a commutator and what is it doing in quantum mechanics.
I have previous knowledge of operators of momentum(p) and energy(E).
Also I have no idea whatsoever about the hamiltonian operator...
PLease i really need help in this one as it's quite an important topic I have been told...
Thank You..
Also It would be greatly helpful if you could tell me as to where can I find study material related to it online...
:)
 
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  • #3


Thanks... and I'm sorry for the premature bumping...
 
  • #4


schumi1991, You'll get a quicker response the next time if you don't...scream!
 
  • #5


yeah I got that... And I again apologize to the forum.. :(
THanx
 

1. What is a commutator in quantum mechanics?

A commutator in quantum mechanics is a mathematical operator that represents the difference between two operators. It is used to determine the relationship between two observables, such as position and momentum, in a quantum system.

2. How is a commutator calculated?

To calculate the commutator of two operators A and B, the following formula is used: [A, B] = AB - BA. This represents the difference between the product of A and B and the product of B and A.

3. What is the physical significance of a non-zero commutator?

A non-zero commutator indicates that the two operators do not commute, meaning that their order of operations matters. This has physical significance in quantum mechanics as it implies that the observables cannot be measured simultaneously with certainty.

4. How does the commutator relate to Heisenberg's uncertainty principle?

The commutator is the mathematical basis for Heisenberg's uncertainty principle, which states that the more precisely one observable is measured, the less precisely the other can be measured. This is due to the non-zero commutator between the two observables.

5. Can a commutator be used to determine the energy spectrum of a quantum system?

Yes, a commutator can be used to determine the energy spectrum of a quantum system. The energy spectrum is related to the eigenvalues of the commutator, which can be calculated using the commutator formula. This allows for the prediction of the possible energy states of a quantum system.

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