Normalizing a Non-Normalized Wavefunction

  • Thread starter Thread starter physixchic
  • Start date Start date
  • Tags Tags
    Wavefunction
Click For Summary
SUMMARY

The discussion focuses on the normalization of a non-normalized wavefunction, specifically the integral \(\int_{-\infty}^\infty |x| e^{-|x|} \, dx\). Participants emphasize the importance of removing absolute value signs from the integrand before proceeding with integration. The correct approach involves rewriting \(|x| e^{-|x|}\) for both positive and negative values of \(x\) and then applying partial integration carefully across appropriate boundaries to avoid complications.

PREREQUISITES
  • Understanding of wavefunctions and their normalization in quantum mechanics
  • Familiarity with integral calculus, particularly improper integrals
  • Knowledge of partial integration techniques
  • Basic concepts of absolute value functions in mathematical expressions
NEXT STEPS
  • Study the process of normalizing wavefunctions in quantum mechanics
  • Learn about improper integrals and their convergence criteria
  • Explore advanced techniques in integration, including integration by parts
  • Review the properties and applications of absolute value functions in calculus
USEFUL FOR

Students and professionals in quantum mechanics, physicists dealing with wavefunctions, and mathematicians focusing on integration techniques.

physixchic
Messages
10
Reaction score
0
I am given a non-normalized wavefunction and asked to normalize it. The function and the attempt will be in:
http://i35.tinypic.com/2vahvuc.jpg
 
Physics news on Phys.org
You are correct that you have to calculate
\int_{-\infty}^\infty |x| e^{-|x|} \, dx
however you are making the step to partial integration too fast. You have two pairs of absolute value signs in your integrand, which you should get rid of first (hint: how can you write |x| e^{-|x|} without absolute value signs when x > 0? And when x < 0?).

When you then do the partial integration you need to evaluate an expression such as the one you had, but between different boundaries which give no problems anymore.
 

Similar threads

  • · Replies 12 ·
Replies
12
Views
2K
  • · Replies 3 ·
Replies
3
Views
2K
  • · Replies 6 ·
Replies
6
Views
4K
Replies
5
Views
2K
  • · Replies 7 ·
Replies
7
Views
3K
Replies
2
Views
2K
Replies
1
Views
2K
  • · Replies 29 ·
Replies
29
Views
2K
Replies
1
Views
2K
Replies
6
Views
4K