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I have an analytical expression f(x) for my density of states, and I have plottet this. Now, I also have a complete list of my Hamiltonians eigenvalues.

When I make a histogram of these eigenvalues, I thought that I should get an exact (non-continuous) copy of my plot of f(x). They have the same form, but they are not to scale, i.e. f(x) has a maximum at ~100, while the histogram has a maximum at ~60.

Is there an error somewhere, or am I wrong to expect that they should be "exact" copies?