- #1
Pruddy
- 64
- 0
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...