1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Stuck on a 'normalisation' step

  1. May 29, 2009 #1
    Hey guys,

    1. The problem statement, all variables and given/known data
    I have an assignment, which is to Solve Schrodinger's equations, for a certain potential distribution, which can be divided up into three regions.

    A solution for one of the regions is of the form: Ae[tex]^{kx}[/tex]



    If you substitute this into Schrodinger's equation (time independant, one dimension) and solve for k, you get this:

    Schrodingers:
    [tex]\frac{-h}{2m} \frac{d^{2}}{dx^{2}} \Psi (x) + Vo \Psi (x) = E \Psi (x)[/tex]

    Solve for k:
    k = [tex]\frac{\sqrt{2mE}}{h}[/tex]

    I know this part is right because I've seen it written on the board a couple of times, and it's also what I get on paper.

    But then there's the next bit, which I don't get. Apparently it's 'normalising k' which I just don't get..

    k = [tex]\frac{\sqrt{2mE}}{h}[/tex]

    [tex]k\overline{^}\overline{}[/tex] = [tex]\frac{\sqrt{2mE}}{h}.\frac{L}{2}[/tex]

    [E] = [tex]\frac{\pi^{2}h^{2}}{2ML^{2}}[/tex]

    k_hat = [tex]\frac{L}{2} . \frac{\sqrt{2m}}{h} . \sqrt{E}[/tex]

    k_hat = [tex]\frac{L}{2} . \frac{\sqrt{2m}}{h} . \sqrt{\frac{E[E]}{[E]}}[/tex]

    k_hat = [tex]\frac{L}{2} . \frac{\sqrt{2m}}{h} . \sqrt{[E]} \sqrt{Ehat} [/tex]

    k_hat = [tex]\frac{\pi}{2} \sqrt{Ehat}[/tex]
    2. Relevant equations

    None.


    3. The attempt at a solution

    If I rearrange k = [tex]\frac{\sqrt{2mE}}{h}[/tex] and make E the subject,

    I get ..

    E = [tex]\frac{h^{2}khat^{2}}{2m}[/tex]

    and maybe this is where I go wrong.. because I assume E = [E] ?

    Subtituting [E] into the second last step in section 2 above yields:

    [tex]khat = \frac{L}{2} khat \sqrt{Ehat}[/tex]

    and that doesn't equal the last step >_<

    EDIT: ahh.. if I use their definition of [E], [E] = [tex]\frac{\pi^{2}h^{2}}{2ML^{2}}[/tex]
    I arrive at the right answer..


    so how did they come up with [E] = [tex]\frac{\pi^{2}h^{2}}{2ML^{2}}[/tex]??
     
    Last edited: May 29, 2009
  2. jcsd
  3. May 29, 2009 #2

    Cyosis

    User Avatar
    Homework Helper

    What is k_hat and what are you trying to achieve, an expression for E?
     
  4. May 29, 2009 #3
    Sorry!! I've edited my above post.. Now it makes more sense :)

    What I'm really after is how did they (my teacher) come up with [E] and what is it?


    k_hat is apparently a normalised k
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Stuck on a 'normalisation' step
  1. Stuck on these (Replies: 1)

Loading...