# Two-dimensional Contour-Plot

I have a quick question:

In a Solid-state Physics lecture, we discussed the so-called tight-binding model. For that, we had the dispersion-relation (which gives us the dependence of the energy $$E$$ wrt $$\vec k$$) $$E(\vec{k}) = E_{\text{at}} - S - 2A\cdot \left[\cos \left( k_x a\right) + \cos\left( k_y a\right)\right].$$

Now, the professor plots the relation (I think only the part in the []-brackets) in Mathematica and apparently obtains the following result: Now, this is what I tried so far:

ContourPlot[-Cos[x] - Cos[y] , {x, -1/2, 1/2}, {y, -1/2, 1/2}]


with the following result: Unfortunately, I neither reproduce the behavior at the edges of the plot, nor the square. Any hint would be deeply appreciated!

(Please don't get confused about the x- and y-label of the first plot; I think all the professor wants to say is that we don't plot $$k_x$$ and $$k_y$$, but rather $$\vec \kappa$$, which is related to $$\vec k$$ with a factor of $$\frac{2\pi}{a}$$.)

• Try expanding the ranges (probably related to the scaling factor of $2\pi/a$): ContourPlot[-Cos[x] - Cos[y], {x, -3, 3}, {y, -3, 3}]. – JimB Jun 21 at 22:39
• Hi JimB, very nice! I strongly suspect that it then should ContourPlot[-Cos[x]-Cos[y], {x, -Pi, Pi}, {y, -Pi, Pi}]. ;-) Thank you! – MathIsFun Jun 22 at 6:38
• Btw, one more question: I would also like Mathematica to show the values of the different colors. Yesterday, I managed it (it was an option called "Business", I think), but now I cannot find that option anymore. :-( – MathIsFun Jun 22 at 6:46