  One can use the generalized uncertainty principle (GUP) to incorporate the
minimum measurable length in quantum gravity. It may be interesting to have a
minimal time interval as well as the minimal length in the relativistic version
of quantum mechanics in the presence of the gravitational effects. In this
paper, we consider a covariant version of the generalized uncertainty principle
to investigate the effects of both the minimal time and the minimal length.
Using the covariant GUP, the energy-momentum dispersion relation is modified.
Starting with the modified dispersion relation, the corrections to the wave
function are obtained and the problems of the particle in a box and the
Hydrogen atom are revisited.
