- #1

Pruddy

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## 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...