Thermodynamic properties and coherent states for the harmonic oscillator in cosmic string space-time with dislocation

We study the problem of a quantum harmonic oscillator in the presence of a repulsive inverse-square potential within a cosmic string spacetime that contains a dislocation. Also, we study how a rotational frame affects the quantum harmonic oscillator plus the repulsive potential within this space-time geometry. For both problems, we find three operators for the radial part of each problem and show that they close the su(1, 1) Lie algebra. From the theory of unitary irreducible representations of the su(1, 1) Lie algebra, we obtain the energy spectrum from an algebraic point of view. Also, we obtain the wave functions, the radial coherent states, and their time evolution. Finally, we calculate the thermodynamic properties for each of these problems.