Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Probabilistic interpretation of wave function

  1. Oct 26, 2008 #1
    1. The problem statement, all variables and given/known data
    a particle moving in one dimension between rigid walls separated by a distance L has the wave function [tex]\Psi[/tex](x)=Asin([tex]\Pi[/tex]x/L), since the particle must remain between the walls, what must be the value of A?


    2. Relevant equations



    3. The attempt at a solution

    Ok so I'm thinking that since the particle has to be between x=0 and x=1, i should set the probability function = to one for these limits on the integral. i'm really confused on how to do that though
     
  2. jcsd
  3. Oct 26, 2008 #2

    G01

    User Avatar
    Homework Helper
    Gold Member

    What must the following integral be equal to according to the probability interpretation of the wave function?

    [tex]\int_0^L\Psi^*\Psi dx=?[/tex]
     
  4. Oct 26, 2008 #3
    1? to get psi* what do i do?

    thanks
     
  5. Oct 27, 2008 #4
    The star means complex conjugate: replaces all [itex]i[/itex]s with [itex]-i[/itex]s. In your case, [itex]\psi^* = A^* sin(\pi x / L)[/itex], but you can take[itex]A[/itex] to be real, making [itex]\psi = \psi^*[/itex].
     
  6. Oct 27, 2008 #5
    okay, thanks a lot
     
  7. Oct 27, 2008 #6

    G01

    User Avatar
    Homework Helper
    Gold Member

    Yes, that integral is equal to 1. You now, need to evaluate that and figure out what A must be for that expression to be true.

    (I have been busy today and I see I'm a little late to respond. I hope you were able to figure it out.)
     
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook