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In this paper, we study the quantum motions of the non-relativistic particles under the influence of the flux field in the background of a point-like global monopole with Kratzer plus generalised Yukawa potential. The solutions of the quantum system under consideration are obtained using the parametric Nikiforov–Uvarov method by employing the Greene–Aldrich approximation scheme in the centrifugal and reciprocal terms that appear in the radial equation. Afterwards, we use another approximation called the Taylor series expansion up to the first order in the exponential terms and solve the radial equation analytically using the confluent hypergeometric function. It is shown that the topological defect of a point-like global monopole influences the eigenvalue solutions of the non-relativistic particles and gets modified by this defect compared to the flat space result with this superposed potential. We also show that the energy eigenvalue of the particles depends on the quantum flux field and thus gets shifted. Finally, we compare the eigenvalue solutions obtain for these two approximations scheme used here and show graphically that the results are different in these schemes.

Quantum effects with Kratzer plus generalised Yukawa potential in a point-like global monopole using different approximation schemes