  The double-well problem for the two-dimensional Dirac equation is solved for
a family of quasi-one-dimensional potentials in terms of confluent Heun
functions. We demonstrate that for a double well separated by a barrier, both
the energy level splitting associated with the wavefunction overlap of well
states, and the gap size of the avoided crossings associated with well and
barrier state repulsion, can be controlled via the parameters of the potential.
The transitions between the two states comprising a doublet, as well as
transitions across the pseudo-gaps are strongly allowed, highly anisotropic,
and for realistic graphene devices can be tuned to fall within the highly
desirable terahertz frequency range.
