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In this paper, we study the covariant form of the non-relativistic Schrödinger-Pauli equation in the spacetime generated by a cosmic string and discuss the solutions of this equation in the presence of interaction between the magnetic dipole momentum and electromagnetic field. We study the influence of the topology on this system. We obtain the solution of radial part as well as the energy levels. We consider all thermodynamic properties of a neutral particle in a magnetic cosmic string background by using an approach based on the partition function method.

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We study the D-dimensional Schrödinger equation for an energy-dependent Hamiltonian that linearly depends on energy and quadraticly on the relative distance. Next, via the Nikiforov-Uvarov (NU) method, we calculate the corresponding eigenfunctions and eigenvalues.