What could be causing my discrepancies?

[enaj]

Homework Statement

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

Homework Equations

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

The Attempt at a Solution

so far I've plotted f(\alpha*a), 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(\alpha*a), since I'm using \alpha*a as my variable, which is related to energy in the same way k is: \sqrt{ 2mE/\hbar^2}

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.

 

[jdwood983]

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?