Quantum Physics - Calculating Commutators

In summary, the conversation discusses the calculation of commutators in quantum physics, specifically those involving x, y, z, and Lx. The speaker is seeking help and clarification on the math involved and the patterns that may exist to make the calculations easier. There is also a mention of applying operators to known eigenfunctions and the relationship between eigenfunctions of different operators. The speaker expresses gratitude for the assistance and plans to seek help from their TA to catch up on missed classes.
  • #1
Bmmarsh
4
0
Quantum Physics -- Calculating Commutators

The problem states:
Calculate the commutators [x,Lx], [y,Lx], [z, Lx], [x, Ly], [y, Ly], [z, Ly]. Do you see a pattern that will allow you to state the commutators of x, y, z with Lz?

Unfortunately, the book that is asking this question is very vague and doesn't go into any of the math involved. Any help pointing me in the right direction would be greatly appreciated.

[Followup Question]:
Repeat the calculation with x,... replaced by px,...

Again, any help would be amazing!
Thanks!
 
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  • #3
I'll try it out

Thanks for your help!
From what you said, I assume that the commutators [x, Lx], [z, Lz], and [y, Ly] should be zero. I'll have to go to my TA to get help with the eigenfunctions of the angular momentum. I missed a week of classes, so I'm just trying to catch up =)

Thanks again.
 

1. What is a commutator in quantum physics?

A commutator in quantum physics is a mathematical operator that represents the difference between two operators. It is used to understand the relationship between physical quantities in quantum systems.

2. How do you calculate commutators?

The commutator of two operators A and B is given by [A,B] = AB - BA. To calculate it, you multiply the two operators in the given order and then subtract the product of the operators in the opposite order.

3. What is the significance of commutators in quantum physics?

Commutators are important in quantum physics because they can help determine the uncertainty in measurements of quantum systems. They also reveal information about the underlying symmetries and properties of the system.

4. What are some examples of commutators in quantum physics?

Some examples of commutators in quantum physics include the position-momentum commutator [x,p] = iħ, the energy-time commutator [H,t] = iħ, and the angular momentum commutator [Lx,Ly] = iħLz.

5. How are commutators related to Heisenberg's uncertainty principle?

Communtators are related to Heisenberg's uncertainty principle because they are used to calculate the uncertainties in measurements of different quantities, such as position and momentum, as described by the principle. The commutator [x,p] determines the minimum uncertainty in these measurements.

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