For a 1D incommensurate Schrödinger toy model, the second-order semiclassical DoS matches momentum-space numerics at small ε, and the residual oscillations at larger ε are traced to harmonic-oscillator levels at band-structure critical points.
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Numerical computation of the density of states of aperiodic multiscale Schr\"odinger operators
For a 1D incommensurate Schrödinger toy model, the second-order semiclassical DoS matches momentum-space numerics at small ε, and the residual oscillations at larger ε are traced to harmonic-oscillator levels at band-structure critical points.