In mathematical physics, the Wu–Sprung potential, named after Hua Wu and Donald Sprung, is a potential function in one dimension inside a Hamiltonian with the potential defined by solving a non-linear integral equation defined by the Bohr–Sommerfeld quantization conditions involving the spectral staircase, the energies and the potential . here a is a classical turning point so , the quantum energies of the model are the roots of the Riemann Xi function and . In general, although Wu and Sprung considered only the smooth part, the potential is defined implicitly by ; with N(x) being the eigenvalue staircase and H(x) is the Heaviside step function.