  We investigate the gravitational effect on Landau levels. We show that the
familiar infinite Landau degeneracy of the energy levels of a quantum particle
moving inside a uniform and constant magnetic field is removed by the
interaction of the particle with a gravitational field. Two independent
approaches are used to solve the relevant Schr\"odinger equation within the
Newtonian approximation. It is found that both approaches yield qualitatively
similar results within their respective approximations. With the goal of
clarifying some results found in the literature concerning the use of a third
independent approach for extracting the quantization condition based on a
similar differential equation, we show that such an approach cannot yield a
general and yet consistent result. We point out to the more accurate, but
impractical, way to use such an approach; a way which does in principle yield a
consistent quantization condition. We discuss how our results could be used to
contribute in a novel way to the existing methods for testing gravity at the
tabletop experiments level as well as at the astrophysical observational level
by deriving the corrections brought by Yukawa-like and power-law deviations
from the inverse-square law. The full relativistic regime is also examined in
detail.
