Particle in a box

  • #1
stunner5000pt
1,447
2
For a particle in a one dimensional infinite squat well of width a, s.t 0<x<a the eignefunctions are given by

[tex] \psi_{x} (x) = N \sin k_{n} x [/tex] for 0 < x < a

where [tex] k_{n} = \frac{n \pi}{a} [/tex] and n = 1,2,3,...

Consider the Fourier sine series for the function f(x) on teh interval 0<x<a
[tex] f(x) = \sum_{n=1,2,3,...} c_{n} \psi_{n} (x) [/tex]

Showthat the coefficients of this series are given by
[tex] c_{n} = \frac{2}{a} \int_{0}^{a} \sin (k_{n} x) f(x) dx [/tex]

do i have to PROVE that the coefficients are given by Cn??

isnt the expression by Cn given by the definition of Cn from teh Foureir series?? Also why is the persiod a? If n was not 1 then the period would not be a, would it/?
 

Answers and Replies

  • #2
StatusX
Homework Helper
2,571
2
You have a definition of f(x), so just plug that into the integral. All of the terms will drop out except the one with c_n. I don't understand your question about the period.
 
  • #3
physics girl phd
937
3
Are you talking about the a in the denominator of the k_n? This puts everything in the right length scale, so the eigenfunction's conditions at the boundary of the box are met. Does that make sense?
 

Suggested for: Particle in a box

Replies
15
Views
285
  • Last Post
Replies
11
Views
678
  • Last Post
Replies
24
Views
1K
Replies
3
Views
394
Replies
9
Views
527
  • Last Post
Replies
8
Views
623
Replies
2
Views
95
Replies
4
Views
238
Top