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Quantum chaos
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=== One-dimensional systems and potential === For the case of one-dimensional system with the boundary condition <math> y(0)=0 </math> the density of states obtained from the Gutzwiller formula is related to the inverse of the potential of the classical system by <math> \frac{d^{1/2}}{dx^{1/2}} V^{-1}(x)=2 \sqrt \pi \frac{dN(x)}{dx} </math> here <math> \frac{dN(x)}{dx} </math> is the density of states and V(x) is the classical potential of the particle, the [[half derivative]] of the inverse of the potential is related to the density of states as in the [[Wu–Sprung potential]].
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