Quantum Meachanics; Normalization in 3D

  1. 1. The problem statement, all variables and given/known data
    (1) For the cubic 3D infinite-well wave function,
    [tex]\psi[/tex](x,y,z) = A sin(n[tex]\pi[/tex]x/L)sin(n[tex]\pi[/tex]y/L)sin(n[tex]\pi[/tex]z/L)
    Show that the correct normalization constant is A = (2/L)[tex]^{3/2}[/tex]



    2. Relevant equations
    Note: The Pi's above are not meant to be superscript, and each n relates to the appropriate x,y,z
    [tex]\int[/tex][tex]\psi[/tex]*[tex]\psi[/tex]dx=1

    3. The attempt at a solution
    I have rearranged for A squared outside of the integral of the three sine functions (as a product) with limits of integration 0 to L. Not going to show it here becaus its long and messy. I am wondering if i need to do a triple (volume integration) or whether there is a shortcut because thats going to be one big, nasty integration :s
    A little guidance would be appreciated,
    Cheers, Joel.
     
  2. jcsd
  3. Avodyne

    Avodyne 1,288
    Science Advisor

    Your triple integral is the product of three single integrals, each of which is the same (except for the name of the dummy integration variable).
     
  4. Ah, thats how it comes to root A cubed. Thankyou.
     
Know someone interested in this topic? Share a link to this question via email, Google+, Twitter, or Facebook

Have something to add?