Evaluating Operators

  • Thread starter Pruddy
  • Start date
  • #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...
 

Answers and Replies

  • #2
Bystander
Science Advisor
Homework Helper
Gold Member
5,390
1,470
checking to see if my answer was right.
Looks good.
 
  • #3
Simon Bridge
Science Advisor
Homework Helper
17,874
1,657
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.
 
  • #4
Pruddy
64
0
Thanks you all so much for your feedback. I am very grateful:).
GOD bless....
 

Suggested for: Evaluating Operators

  • Last Post
Replies
18
Views
765
Replies
3
Views
280
  • Last Post
2
Replies
43
Views
1K
Replies
3
Views
463
Replies
1
Views
319
  • Last Post
Replies
7
Views
313
  • Last Post
Replies
5
Views
297
Replies
1
Views
181
Replies
3
Views
166
Top