  This work investigates in which form quantities with Planck dimensions occur
already in the common quantum theory with local Lorentz symmetry. Since such
Planck quantities as Planck length or Planck mass involve the Planck constant
h, the velocity of light c and the Newton gravitational constant G, the
relativistic Dirac equation (h, c) in the Newtonian gravitational potential (G)
can be considered as a test theory. The evaluation of the break-off condition
of the power series of the radial energy eigenfunctions of a purely
gravitational atom leads to exact terms for the energy eigenvalues E for
various special cases of the quantum numbers N, k and n = N + |k|. It turns out
that a meaningful atom model, based solely on Newtonian gravitational forces,
can result if, inter alia, the test mass m in the gravitational field of the
mass M is selected to be smaller than the Planck mass.
