Solutions of Schrödinger's equation are presented for two-particle system interacting through generalized exponential cosine screened Coulomb potential. Solutions are computed for several values of screening parameters. In the present context, Ritz variation method is used with hydrogenic wave function as a trial wave function. The bound energies are derived from an energy equation which contains one unknown variational parameter. To calculate the variational parameter numerically fixed-point iteration scheme is used. The calculated energy eigenvalues for exponential cosine screened Coulomb potential agree excellently with the available other theoretical results. Under screening, all energy levels are shifted away from their unscreened values toward the continuum. The radial wave functions, radial probability distribution functions are presented for different screening parameters.

## Keywords

- Exponential cosine Coulomb potential;
- One-electron system;
- Variational method