  Several approaches to quantum gravity lead to nonlocal modifications of
fields' dynamics. This, in turn, can give rise to nonlocal modifications of
quantum mechanics at non-relativistic energies. Here, we analyze the nonlocal
Schr\"{o}dinger evolution of a quantum harmonic oscillator in one such
scenario, where the problem can be addressed without the use of perturbation
theory. We demonstrate that although deviations from standard quantum
predictions occur at low occupation numbers, where they could potentially be
detected or constrained by high-precision experiments, the classical limits of
quantum probability densities and free energy remain unaffected up to energies
comparable with the nonlocality scale. These results provide an example of
nonlocal quantum dynamics compatible with classical predictions, suggesting
massive quantum objects as a promising avenue for testing some phenomenological
aspects of quantum gravity.
