How to Demonstrate [Lk, r^2] = 0?

Thread starter jc09
Start date Apr 23, 2009
Tags

Angular Angular momentum Momentum

In summary, a commutator is a mathematical operation that measures the degree of commutativity between two variables or quantities. Lk and r^2 are compared in the commutator, with Lk representing the Laplace transform and r^2 representing squaring a number. Proving that the commutator of Lk and r^2 equals 0 is important as it shows that these operations are commutative, and the order in which they are performed does not affect the final result. The commutator of Lk and r^2 is calculated using the formula [Lk, r^2] = Lk(r^2) - r^2(Lk), and a non-zero result means that these operations

Apr 23, 2009

jc09

Homework Statement

Show that [ Lk , r^2] = 0

Homework Equations

The Attempt at a Solution

know that L=r x p=r x(-ih(bar)V)

Physics news on Phys.org

Apr 23, 2009

Cyosis

Homework Helper

With the k I take it you mean the third component?

Lets write it like this [Lz,r^2]=[Lz,x^2+y^2+z^2]=[Lz,x^2]+[Lz,y^2]+[Lz,z^2]. Can you work out these three commutators?

FAQ: How to Demonstrate [Lk, r^2] = 0?

What is a commutator?

A commutator is a mathematical operation used to determine the degree of commutativity (or lack thereof) between two variables or quantities. In simpler terms, it measures how much the order of two operations affects the final result.

What is Lk and r^2 in relation to the commutator?

Lk and r^2 are variables or quantities that are being compared in the commutator. Lk represents the operation of taking the Laplace transform of a function, while r^2 represents the operation of squaring a number.

Why is it important to prove that Lk and r^2 commutator equals 0?

Proving that the commutator of Lk and r^2 equals 0 is important because it indicates that these two operations are commutative, meaning that the order in which they are performed does not affect the final result. This can be useful in various mathematical and scientific calculations.

How is the commutator of Lk and r^2 calculated?

The commutator of Lk and r^2 is calculated using the formula [Lk, r^2] = Lk(r^2) - r^2(Lk). This means taking the Laplace transform of r^2 and subtracting the result from squaring the Laplace transform of a function. The result should equal 0 for the commutator to be proven.

What implications does a non-zero commutator of Lk and r^2 have?

A non-zero commutator of Lk and r^2 means that these two operations do not commute, and the order in which they are performed does affect the final result. This can complicate calculations and may require further analysis or adjustments in mathematical models.