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Kronig-penney E-k diagram

  1. Oct 22, 2009 #1
    1. The problem statement, all variables and given/known data

    reproduce the kronig-penney E-k diagram (nothing more specific than that)


    2. Relevant equations
    f([tex]\alpha*a[/tex])=P*SIN([tex]\alpha*a[/tex])/([tex]\alpha*a[/tex])+COS([tex]\alpha*a[/tex])
    where P is the strength of the potential (I've assumed that it's 3[tex]\pi[/tex]/2)
    and -1<=f([tex]\alpha*a[/tex])<=1

    3. The attempt at a solution
    so far I've plotted f([tex]\alpha*a[/tex]), and as far as I can tell it looks right. But when I try to plot the allowed energy values from that graph against the k values, I get a graph that's a little too regular (though it does have band gaps) and it has no allowed states below ~k=0.6
    I may be calculating k wrong. As I understand it, it's equal to the square root of the the energy from the graph of f([tex]\alpha*a[/tex]), since I'm using [tex]\alpha*a[/tex] as my variable, which is related to energy in the same way k is: [tex]\sqrt{ 2mE/\hbar^2}[/tex]

    I've attached the graphs I have so far (the spreadsheet I used to calculate them is much too big).

    Can anyone see where I might have gone wrong? I've replotted this many times and I can't seem to find it.
     

    Attached Files:

    Last edited: Oct 22, 2009
  2. jcsd
  3. Oct 23, 2009 #2
    My guess is that your software isn't capable of handling precision calculations. I'd recommend using another program, rather than OpenOffice/MS Excel.

    As far as the graphs go, they look more or less right; though that non-existence of states below k=0.6 is a little strange--have you changed your value of P to see what effect that has on the graph?
     
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