# Show [J2, J+] = 0 - Homework Solution

• NewtonApple
In summary, "Show [J2, J+] = 0 - Homework Solution" is a notation in quantum mechanics asking for a proof that the commutator of the operators J2 and J+ is equal to zero. This is significant because it represents the angular momentum and shows that these operators can be measured simultaneously without uncertainty. To solve this problem, a strong understanding of quantum mechanics principles and mathematical techniques is necessary. The commutator [J2, J+] = 0 has various applications in quantum mechanics and there are other important commutators, such as [x, p] = iħ and [L, S] = iħ.
NewtonApple

## Homework Statement

To show [J2, J+] = 0

2. Homework Equations

J+ = Jx + i Jy

[J2, Jx ] = 0

[J2, Jy ] = 0

## The Attempt at a Solution

Step 1: L.H.S. = [J2, J+]

Step 2: L.H.S. = [J2, Jx + i Jy ]

Step 3: L.H.S. = [J2, Jx ] + i [J2, Jy ]

Step 4: L.H.S. = 0 + 0

Step 5: L.H.S. = 0

L.H.S. = R.H.S.

I'm kinda confuse about 'Step 3'. Can we take out the 'i' from whole bracket? If yes, then do I have to give any reason for it?

Go ahead and write out the full commutator in step 2. What do you get?

## What does "Show [J2, J+] = 0 - Homework Solution" mean?

"Show [J2, J+] = 0 - Homework Solution" is a mathematical notation that represents a specific problem or concept in quantum mechanics. It is asking for a proof or demonstration that the commutator of the operators J2 and J+ is equal to zero.

## What is the significance of showing [J2, J+] = 0?

The commutator [J2, J+] = 0 is significant because it represents the angular momentum in quantum mechanics. It shows that the operators J2 and J+ commute, meaning that they can be measured simultaneously with no uncertainty. This is a fundamental concept in quantum mechanics and has important implications in understanding the behavior of particles at the quantum level.

## How can I solve this problem?

To solve this problem, you will need to have a strong understanding of the principles of quantum mechanics and how to manipulate operators. You will also need to use mathematical techniques such as commutator algebra. It is recommended to consult textbooks or seek guidance from a mentor or instructor if you are having difficulty solving this problem.

## What are some applications of the commutator [J2, J+] = 0?

The commutator [J2, J+] = 0 has various applications in quantum mechanics, such as in the study of angular momentum and spin, as well as in the formulation of quantum mechanical models and equations. It also plays a crucial role in quantum mechanics experiments and technologies.

## Are there any other important commutators in quantum mechanics?

Yes, there are many other important commutators in quantum mechanics, such as [x, p] = iħ, which represents the uncertainty relation between position and momentum. Other examples include [H, p] = 0, which represents the conservation of momentum in a system with a time-independent Hamiltonian, and [L, S] = iħ, which represents the commutation relation between the orbital and spin angular momentum operators.

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