Evaluating Operators: ABF(x) and BAF(x)

[Pruddy]

Homework Statement

Given the operator A = d/dx and B = x and the function f(x) = xe^(-ax)

evaluate : ABF(x) and BAF(x)

Do these operators commute (yes/No)

Homework Equations

[A,B]F(x) = ABF - BAF = 0 ; means they commute

The Attempt at a Solution

[A,B]F(x) = ABF - BAF = 0
=d/dx(x^2e^-ax) - x d/dx (xe^-ax)
=2xe^-ax - ax^2e^-ax - xe^-ax + ax^2e^-ax
= 2xe^-ax - xe^-ax

No they do not commute [B,A]F(x) = BAF - ABF = 0
= x d/dx(xe^-ax) - d/dx (x^2e^-ax)
= xe^-ax - x^2ae^-ax - 2xe^-ax + x^2ae^-ax
= xe^-ax - 2xe^-ax

They do not commute...I was checking to see if my answer was right. Thanks in advance...

 

[Bystander]

checking to see if my answer was right.

Looks good.

 

[Simon Bridge]

Seems reasonable - but needs a cleanup.
You should either keep the =0 all the way down (using implied signs on the left of each line) or leave it off the first line.
You need to comment that the last line does not equal zero (or that it is false if you kept the =0 part).

The assignment expects you to evaluate ABF and BAF separately and notice that they are not the same.

 

[Pruddy]

Thanks you all so much for your feedback. I am very grateful:).
GOD bless...