A Numerical Toolkit for Hydrogenic Binding Energies and Wave Functions in 2D

We present a numerical toolkit in Python, readily deployable on Google Colab, for solving the two-dimensional Schrödinger equation in momentum space for hydrogenic systems with a soft-Coulomb potential. The approach reformulates the bound-state problem as a Lippmann–Schwinger integral equation, from which binding energies and wavefunctions are obtained for the ground state and nine excited states across a broad range of the softening parameter a. For the standard Coulomb limit (a=0), the computed binding energies agree with analytical values to within 1.0%. For finite a, ground-state energies show excellent agreement with configuration-space results, with discrepancies below 0.1%.