  Most approaches towards a quantum theory of gravitation indicate the
existence of a minimal length scale of the order of the Planck length. Quantum
mechanical models incorporating such an intrinsic length scale call for a
deformation of Heisenberg's algebra resulting in a generalized uncertainty
principle and constitute what is called gravitational quantum mechanics. Here
we adopt the pseudo or g-calculus to study various models of gravitational
quantum mechanics. The free time evolution of a Gaussian wave packet is
investigated as well as the spectral properties of a particle bound by an
external attractive potential. Here the cases of a box with finite width and
infinite walls, an attractive potential well of finite depth and a delta-like
potential are considered.
