I am trying to calculate the density of energy states in a two dimensional box. The way my professor did this is by first calculating the amount of states with their energy less than some energy e and taking its derivative with respect to e. In order to see how many energy states there are with energy less than e we are first calculating the amount of momentum states with a k vector less than some k and then translating it into the corresponding condition for energy.(adsbygoogle = window.adsbygoogle || []).push({});

There is one step in the derivation where my professor makes a jump which I do not understand, and I need some help with. I understand that for some given k vector in 2-dimensions, it has magnitude

k = √(k_{x}^{2}+ k_{x}^{2}) where k_{x}= π n_{x}/L_{x}and the same for y.

she then makes the jump that the amount of states with k vectors of magnitude less than some given k is

(1/4)(πk^{2})/(π/L_{x}+ π/L_{y})

I do not understand how she arrived at this, any help would be appreciated

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# Density of states in 2 dimensional box

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