  We examine the nonperturbative effect of maximum momentum on the relativistic
wave equations. In momentum representation, we obtain the exact eigen-energies
and wavefunctions of one-dimensional Klein-Gordon and Dirac equation with
linear confining potentials, and the Dirac oscillator. Bound state solutions
are only possible when the strength of scalar potential are stronger than
vector potential. The energy spectrum of the systems studied are bounded from
above, whereby classical characteristics are observed in the uncertainties of
position and momentum operators. Also, there is a truncation in the maximum
number of bound states that is allowed. Some of these quantum-gravitational
features may have future applications.
