Manipulate Commutator Relations in Quantum Mechanics - Help Needed

In summary, the conversation discusses the difficulty in finding a reliable resource on the topic of manipulating commutator relations in quantum mechanics. Specifically, the person is looking for information on when they can rearrange the expression [AB,C] into A[B,C] and whether it should be done as A[B,C]+[B,C]A or [A,C]B + A[B,C]. They mention that they are having trouble finding online resources that explain these concepts and ask for help.
  • #1
Dishsoap
1,017
310
This is not a homework question, I just can't find a good resource on this topic.

I am working in quantum mechanics on commutator relations. My book (Griffiths) lacks information on how to manipulate the commutator relations.

For instance, when I have [AB,C], when can I make it A[B,C]? Or is it A[B,C]+[B,C]A? I can't find an online resource that explains these things. Help please!
 
Physics news on Phys.org
  • #2
samnorris93 said:
This is not a homework question, I just can't find a good resource on this topic.

I am working in quantum mechanics on commutator relations. My book (Griffiths) lacks information on how to manipulate the commutator relations.

For instance, when I have [AB,C], when can I make it A[B,C]? Or is it A[B,C]+[B,C]A? I can't find an online resource that explains these things. Help please!

Do things like the product rule in differentiation:

[AB,C] = [A,C]B + A[B,C]
 

What is a commutator in quantum mechanics?

A commutator in quantum mechanics is a mathematical operation that describes the non-commutativity of two operators. It is represented by the symbol [A,B] and is defined as AB-BA.

Why is it important to manipulate commutator relations in quantum mechanics?

Manipulating commutator relations allows us to understand how different operators in quantum mechanics interact with each other. This is crucial in predicting the behavior of quantum systems and making accurate measurements.

What are some common commutator relations in quantum mechanics?

Some common commutator relations in quantum mechanics include the position-momentum commutator [x,p]=iℏ, the angular momentum commutator [Lx,Ly]=iℏLz, and the energy-time commutator [H,t]=-iℏ.

How do commutator relations affect the uncertainty principle?

The uncertainty principle states that the more precisely we know the value of one observable, the less precisely we can know the value of another. Commutator relations play a role in this principle, as they determine the maximum possible accuracy of measurements for certain pairs of observables.

Are there any practical applications of manipulating commutator relations in quantum mechanics?

Yes, manipulating commutator relations is essential in the development and understanding of quantum technologies such as quantum computing and quantum cryptography. It also has applications in fields such as chemistry, material science, and cosmology.

Similar threads

Deriving the commutation relations of the Lie algebra of Lorentz group
    • Advanced Physics Homework Help
Replies
3
Views
2K
Beam Splitter Inputs and Commutting Modes
    • Advanced Physics Homework Help
Replies
1
Views
1K
General commutation relations for quantum operators
    • Advanced Physics Homework Help
Replies
1
Views
2K
Commutation and Measurement of Observables
    • Advanced Physics Homework Help
Replies
4
Views
1K
Commutation relations in SUSY
    • Advanced Physics Homework Help
Replies
1
Views
1K
Particle in a cylindrically symmetric potential (Quantum mechanics)
    • Advanced Physics Homework Help
Replies
5
Views
1K
String Theory-Virasoro Generators -- show commutator relation
    • Advanced Physics Homework Help
Replies
4
Views
2K
Quantum Field Theory, Momentum Space Commutation Relations
    • Advanced Physics Homework Help
Replies
1
Views
2K
I Applications of measurement of commutativity
    • Topology and Analysis
Replies
5
Views
1K
Quantum operators and commutation relations
    • Advanced Physics Homework Help
Replies
8
Views
2K

Hot Threads

Recent Insights

Back
Top