The single-particle level density
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The single-particle level density book
One fundamental feature of the level density is that it can always be decomposed into a smooth and an oscillating part. The level density contains all the information about the irregularities of the quantum spectrum. On the average, it has a smooth energy dependence which is determined by the number of degrees of freedom and the degeneracies of the singleparticle levels, given by the symmetries of the Hamiltonian. The trace formula represents a Fourier decomposition of the oscillating part of the level density. It gives the basis for many interesting interpretations of quantum phenomena in terms of classical orbits. The smooth level density is in many analytical cases found to be identical with the extended Thomas-Fermi result. That F(E) is proportional to the classical action may intuitively be understood at this point for a one-dimensional system with dn = 1.