Accurate calculation of the bound states of Hellmann potential

Bound states of the Hellmann potential, which is a superposition of the attractive Coulomb ($-A/r$) and the Yukawa ($Be^{-Cr}/r$) potential, are calculated by using a generalized pseudospectral method. Energy eigenvalues accurate up to thirteen to fourteen significant figures, and densities are obtained through a nonuniform, optimal spatial discretization of the radial Schrödinger equation. Both ground and excited states are reported for arbitrary values of the potential parameters covering a wide range of interaction. Calculations have been made for higher states as well as for stronger couplings. Some new states are reported here for the first time, which could be useful for future works. The present results are significantly improved in accuracy over all other existing literature values and offers a simple, accurate and efficient scheme for these and other singular potentials in quantum mechanics.

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