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

A particle in a box.

  • Thread starter Kruum
  • Start date
  • #1
220
0

Homework Statement



A particle is in a box of width L. Calculate the probability to find the particle in the region [L/4, 3L/4] when the particle is a) in the ground state b) in the first excited state.

Homework Equations



(2/L)sin(n*π*x/L)^2 dx is the probability in [x, x+dx]

The Attempt at a Solution



Integrating that gives me 2/L[x/2-[L/(4π)]sin(2n*π*x/L)], boundaries being L/4 and 3L/4. For a) n=1 and b) n=2, right? After I plug in the values, I get value greater than 1. Where have I gone wrong?

Hopefully this is readable, no LaTeX. :cry:
 

Answers and Replies

  • #2
dx
Homework Helper
Gold Member
2,011
18
The probability density is (2/L)sin²(nπx/L) for even n and (2/L)cos²(nπx/L) for odd n.

EDIT: Sorry, this is only if you take the boundaries of the box to be -L/2 and L/2.
 
Last edited:
  • #3
125
1
No, it's the same formula for all n!
After integration i got 2/L[x/2-[L/(4π n)]sin(2n*π*x/L)]
For n = 1 -> (2+π)/(2π)
for n = 2 -> 1/2
 
  • #4
dx
Homework Helper
Gold Member
2,011
18
Yes sorry, I took the boundaries to be -L/2 and L/2.
 
  • #5
220
0
Thanks for the replies, guys! I forgot the one n in my first post. I found out my error was in the easy stuff after the integration, I'd done a mistake in adding fractions. :redface:
 

Related Threads for: A particle in a box.

  • Last Post
Replies
2
Views
589
  • Last Post
Replies
4
Views
1K
  • Last Post
Replies
3
Views
2K
  • Last Post
Replies
7
Views
2K
  • Last Post
Replies
8
Views
1K
  • Last Post
Replies
13
Views
7K
  • Last Post
Replies
6
Views
1K
  • Last Post
Replies
4
Views
1K
Top