A spinless particle coupled covariantly to a uniform magnetic field parallel to the string in the background of the rotating cosmic string is studied. The energy levels of the electrically charged particle subject to the Klein–Gordon oscillator are analyzed. Afterwards, we consider the case of the position-dependent mass and show how these energy levels depend on the parameters in the problem. Remarkably, it shows that for the special case, the Klein–Gordon oscillator coupled covariantly to a homogeneous magnetic field with the position-dependent mass in the rotating cosmic string background has the similar behaviors to the Klein–Gordon equation with a Coulomb-type configuration in a rotating cosmic string background in the presence of an external magnetic field.

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In this paper, a charged half-spin particle depicted by the Dirac equation in the presence of a uniform magnetic field and a mixed potential are analyzed in the rotating cosmic string space–time. In order to facilitate this study, we assume that the symmetrical center of the potential is on the string and the magnetic field is parallel to the string. Based on the functional analysis method, we obtain the energy eigenvalues for different physical situations. It shows that the energy levels of the system depend explicitly on the angular deficit [Formula: see text] and the rotational parameter [Formula: see text] which characterize the global structure of the metric in the space–time of the rotating cosmic string.

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The spin-one Duffin-Kemmer-Petiau (DKP) oscillator under a magnetic field in the presence of the minimal length in the noncommutative coordinate space is studied by using the momentum space representation. The explicit form of energy eigenvalues is found, and the eigenfunctions are obtained in terms of the Jacobi polynomials. It shows that for the same azimuthal quantum number, the energy E increases monotonically with respect to the noncommutative parameter and the minimal length parameter. Additionally, we also report some special cases aiming to discuss the effect of the noncommutative coordinate space and the minimal length in the energy spectrum.