Klein–Gordon equation

Laguerre polynomials

Physics

Eigenfunction

Yukawa potential

Meteorology

Nonlinear system

Eigenvalues and eigenvectors

Energy (signal processing)

Work (physics)

Bar (unit)

Scattering

Meson

Woods–Saxon potential

Quantum electrodynamics

Mathematical physics

Quantum mechanics

Indian Journal of Physics

In this work, we obtain the Klein–Gordon equation solutions for the Yukawa potential using the Nikiforov–Uvarov method. The energy eigenvalues are obtained both in relativistic and non-relativistic regime. The corresponding eigenfunction are obtained in terms of Laguerre polynomial. We applied the present results to calculate heavy-meson masses of charmonium $$ c\bar{c} $$ c c ¯ and bottomonium $$ b\bar{b} $$ b b ¯ , and we got the numerical values for states 1S–1F. The results are in good agreement with experimental data and the work of other researchers.

Approximate solutions of D-dimensional Klein–Gordon equation with Yukawa potential via Nikiforov–Uvarov method