Evaluating Commutator [x, p^2]: Need Help!

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In summary, a commutator is an operation that measures how two operators interact with each other. Evaluating the commutator [x, p^2] is important for understanding quantum mechanics and calculating physical quantities such as the uncertainty principle. To evaluate it, a mathematical formula is used and the resulting value can tell us about the uncertainty in a quantum system. The commutator can be zero, indicating that the operators commute and do not affect each other's uncertainty.
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syang9
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i've been trying to evaluate this commutator the 'easy' way--that is, without using the definition of the momentum operator. the farthest i got was trying to use this rule..

[A, BC] = [A, B]C + B[A, C]

so..
[x, p^2] = [x, p]p + p[x, p]

so i guess i get 2ihp. but that doesn't make sense, b/c there's an operator in that result. so i don't get what else I'm supposed to do. can anyone help me out?
 
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There's no reason you shouldn't have an operator in the result.

What you have done is fine.
 

Related to Evaluating Commutator [x, p^2]: Need Help!

1. What is a commutator?

A commutator is an operation in mathematics and physics that measures how two operators (such as x and p^2) interact with each other. It is defined as the difference between the product of the operators and the product of the operators in reverse order.

2. Why is it important to evaluate the commutator [x, p^2]?

Evaluating the commutator [x, p^2] is important because it helps us understand the fundamental properties of quantum mechanics. It also allows us to calculate important physical quantities, such as the uncertainty principle, which is crucial in many areas of physics.

3. How do you evaluate the commutator [x, p^2]?

To evaluate the commutator [x, p^2], we use a mathematical formula that involves the operators x and p^2. This formula is: [x, p^2] = x*p^2 - p^2*x. We then substitute the specific values of x and p^2 into the formula and solve for the commutator.

4. What does the commutator [x, p^2] tell us about the system?

The commutator [x, p^2] tells us about the uncertainty in the measurement of position and momentum in a quantum system. It is related to the Heisenberg uncertainty principle, which states that the more precisely we know the position of a particle, the less precisely we can know its momentum, and vice versa.

5. Can the commutator [x, p^2] be zero? What does this mean?

Yes, the commutator [x, p^2] can be zero for certain values of x and p^2. This means that the operators x and p^2 commute with each other, and their measurements do not affect each other's uncertainty. This is known as a compatible pair of operators and is a rare occurrence in quantum mechanics.

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