• Support PF! Buy your school textbooks, materials and every day products Here!

Wave function

  • Thread starter roshan2004
  • Start date
  • #1
140
0
A particle moving on a straight line is described by [tex]\psi(x)=\frac{1+ix}{1+ix^2}[/tex].
Where is the particle likely to be found?
I took the derivative of probability density with respect to x and equated it to 0. I got my answer to be x=0.643,-0.643,1.554i and -1.554i.
Please tell me whether I am right or wrong or are there any other methods to solve this problem or not?
 

Answers and Replies

  • #2
dx
Homework Helper
Gold Member
2,011
18
There is no reason for the expectation value to be at a stationary point of the probability density.

You have to evaluate the integral <x> = ∫ψ*(x)xψ(x)dx = ∫xP(x)dx.
 
  • #3
140
0
But the question is about maximum probability of finding the particle, isn't it?
 
  • #4
dx
Homework Helper
Gold Member
2,011
18
"Where is the particle likely to be found" usually means that they want you to find the expectation value of x.
 
  • #5
dx
Homework Helper
Gold Member
2,011
18
Unless the exact wording of the question was "where is the particle most likely to be found". Then you would find the x which maximises P(x).
 
  • #6
140
0
So if the question is where the particle is most likely to be found, is my answer correct.
 
  • #7
dx
Homework Helper
Gold Member
2,011
18
x is a real number, how did you get imaginary values?
 
  • #8
140
0
By factorising
 
  • #9
dx
Homework Helper
Gold Member
2,011
18
  • #10
140
0
Now I finally got it, thanks dx
 

Related Threads on Wave function

Replies
1
Views
8K
  • Last Post
Replies
2
Views
1K
  • Last Post
Replies
3
Views
4K
  • Last Post
Replies
8
Views
9K
  • Last Post
Replies
7
Views
1K
  • Last Post
Replies
3
Views
1K
  • Last Post
Replies
3
Views
2K
  • Last Post
Replies
2
Views
1K
  • Last Post
Replies
1
Views
1K
  • Last Post
Replies
3
Views
2K
Top