  The variety of bi-confluent Heun potentials for a stationary relativistic
wave equation for a spinless particle is presented. The physical potentials and
energy spectrum of this wave equation are related to those for a corresponding
Schr\"odinger equation in the sense that all the potentials derived for the
latter equation are also applicable for the wave equation under consideration.
We show that in contrast to the Schr\"odinger equation the characteristic
spatial length of the potential imposes a restriction on the energy spectrum
that directly reflects the uncertainty principle. Studying the
inverse-square-root bi-confluent Heun potential, it is shown that the
uncertainty principle limits, from below, the principal quantum number for the
bound states, i.e., physically feasible states have an infimum cut so that the
ground state adopts a higher quantum number as compared to the Schr\"odinger
case.
