  We investigate non-inertial effects induced by a rotating frame on a
non-relativistic quantum harmonic oscillator as well as of the topology
associated to a screw dislocation, which corresponds to a distortion of a
vertical line into a vertical spiral. To do this, we obtain the analytical
solutions of the time-independent Schr\"odinger equation for this harmonic
oscillator potential in this background. The expressions for the energy
spectrum are obtained and the solutions for four quantum states, namely
$n=0,1,2$ and $3$, are analysed. Our results show that the presence of the
topological defect (screw dislocation) as well the fact that we are analysing
the system from the point of view of a rotating frame, changes the solutions of
Schr\"odinger equation and the corresponding spectrum. Now these quantities
depend on the angular velocity of the rotating frame, $\Omega$, and also on the
parameter $\beta$, which codifies the presence of the screw dislocation.
Particularly, with respect to the energy spectrum of the system the changing is
such that when $\Omega$ increases, the energy can increase or decrease
depending on the values we assign to the eigenvalues of the angular and linear
momenta. Additionally, we observe that the values of the parameter $\beta$ that
characterizes the screw dislocation causes a shift in the energy spectrum.
