Question in variational method (QM)

  • Thread starter Safinaz
  • Start date
  • #1
220
3

Homework Statement



Hi, in this book " [Nouredine_Zettili]_Quantum_Mechanics_Concepts ", Eq. (9.133)

Homework Equations



I don't know how the second line

upload_2015-9-11_1-25-15.png


had come from the first line:


upload_2015-9-11_0-42-50.png



The Attempt at a Solution




I got only two terms such that:

$$ < \psi_0| H | \psi_0 > = A^2 \int^{+\infty}_{-\infty} \Big( - \frac{2\alpha^2 h^2}{m} e^{-2\alpha x^2} + \frac{1}{2} m \omega^2 x^2 e^{-2\alpha x^2} \Big) dx $$


So what I missed ?
 

Attachments

  • upload_2015-9-11_0-39-53.png
    upload_2015-9-11_0-39-53.png
    44.5 KB · Views: 387
  • upload_2015-9-11_0-44-14.png
    upload_2015-9-11_0-44-14.png
    32.7 KB · Views: 379
  • upload_2015-9-11_0-44-23.png
    upload_2015-9-11_0-44-23.png
    32.7 KB · Views: 395
Last edited:

Answers and Replies

  • #2
35,442
11,883
I fixed the images in your post.

The first derivative of ##e^{-\alpha x^2}## gives ##-2\alpha x e^{-\alpha x^2}##, the second derivative leads to ##(-2\alpha + 4\alpha^2 x^2) e^{-\alpha x^2}## and the second summand should give the missing term.
 
  • #3
220
3
Yap ..
 

Related Threads on Question in variational method (QM)

Replies
3
Views
1K
  • Last Post
Replies
3
Views
1K
  • Last Post
Replies
0
Views
1K
  • Last Post
Replies
1
Views
2K
Replies
8
Views
1K
Replies
17
Views
3K
  • Last Post
Replies
1
Views
2K
Replies
1
Views
1K
  • Last Post
Replies
1
Views
2K
  • Last Post
Replies
5
Views
821
Top