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enaj
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Homework Statement
reproduce the kronig-penney E-k diagram (nothing more specific than that)
Homework 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
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.
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