  We present an extensive numerical study of spectral statistics and
eigenfunctions of quantized triangular billiards. We compute two million
consecutive eigenvalues for six representative cases of triangular billiards,
three with generic angles with irrational ratios with $\pi$, whose classical
dynamics is presumably mixing, and three with exactly one angle rational with
$\pi$, which are presumably only weakly mixing or even only non-ergodic in case
of right-triangles. We find excellent agreement of short and long range
spectral statistics with the Gaussian orthogonal ensemble of random matrix
theory for the most irrational generic triangle, while the other cases show
small but significant deviations which are attributed either to scarring or
super-scarring mechanism. This result, which extends the quantum chaos
conjecture to systems with dynamical mixing in the absence of hard (Lyapunov)
chaos, has been corroborated by analysing distributions of phase-space
localisation measures of eigenstates and inspecting the structure of
characteristic typical and atypical eigenfunctions.
