I'm getting the eigenvalues of a randomly generated hermitian matrix distributed like a normal probabilistic distribution(crowded in the middle values ) but my sir told me that it should be a semicircle , not a bell shaped one.
(not enough rep to upload the plot image, sorry)
I think you were told wrong. The values should indeed approach the semicircle law, but only when the size goes to infinity (and I think that you need some control on the variance of the entries, but I don't really recall that now).