Normalizing Basics

  • Thread starter laser123
  • Start date
  • #1
21
0
How does you normalize a function? Could someone explain it very basically and give an example.
 

Answers and Replies

  • #2
368
12
In Quantum Mechanics, when we talk about normalizing a function, we mean that we want its integral over all space to be equal to 1. So a function is normalized if [itex]\int^\infty_{-\infty}f(x)\:dx = 1[/itex]

If a function is not normalized, then we can normalize it by dividing the function by whatever its total integral is. So if we define [itex]A = \int^\infty_{-\infty}f(x)\:dx[/itex], and we define a new function [itex]f'(x) = \frac{f(x)}{A}[/itex], then by definition, [itex]\int^\infty_{-\infty}f'(x)\:dx = 1[/itex], so [itex]f'(x)[/itex] is normalized.
 
  • #3
21
0
Thank you! :D
 
  • #4
368
12
You're welcome, glad to help!

Also, I should point out that what I gave above was a very generic definition of normalization. In the specific case of quantum mechanics, what we're usually normalizing is the probability density, which is the magnitude squared of the wavefunction. So in practice, the way that you will usually see normalization conditions written is [itex]\int^\infty_{-\infty}|\Psi(x)|^2\:dx = 1[/itex].
 

Related Threads on Normalizing Basics

Replies
9
Views
1K
Replies
14
Views
2K
  • Last Post
Replies
2
Views
2K
  • Last Post
Replies
3
Views
5K
  • Last Post
Replies
5
Views
13K
  • Last Post
Replies
3
Views
1K
  • Last Post
Replies
4
Views
568
  • Last Post
Replies
6
Views
3K
  • Last Post
Replies
2
Views
1K
Top