  We present the exact solution of the 1D Dirac equation for the
inverse-square-root potential $1/\sqrt{x}$ for several configurations of
vector, pseudo-scalar and scalar fields. Each fundamental solution of the
problem can be written as an irreducible linear combination of two Hermite
functions of a scaled and shifted argument. We derive the exact equations for
bound-state energy eigenvalues and construct accurate approximations for the
energy spectrum.
