Bound state equivalent potentials with the Lagrange mesh method

Abstract

The Lagrange mesh method is a very simple procedure to accurately solve eigenvalue problems starting from a given nonrelativistic or semirelativistic two-body Hamiltonian with local or nonlocal potential. We show in this work that it can be applied to solve the inverse problem, namely, to find the equivalent local potential starting from a particular bound state wave function and the corresponding energy. In order to check the method, we apply it to several cases which are analytically solvable: the nonrelativistic harmonic oscillator and Coulomb potential, the nonlocal Yamaguchi potential and the semirelativistic harmonic oscillator. The potential is accurately computed in each case. In particular, our procedure deals efficiently with both nonrelativistic and semirelativistic kinematics.

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References in corpus (9)

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Cited by in corpus (7)

• Accurate solution of the Dirac equation on Lagrange meshes
• Excited flux tube from $q\bar{q}g$ hybrid mesons
• Effective potential between two gluons from the scalar glueball
• Lagrange-mesh calculations in momentum space
• Lagrange-mesh calculations and Fourier transform
• Hyperspherical-coordinate approach to the spectra and decay widths of hybrid quarkonia
• Effective potential between two transverse gluons from lattice QCD