  We consider the effect of quantum spin fluctuations on the ground state
properties of the Heisenberg antiferromagnet on an anisotropic triangular
lattice using linear spin-wave theory. This model should describe the magnetic
properties of the insulating phase of the kappa-(BEDT-TTF)_2 X family of
superconducting molecular crystals. The ground state energy, the staggered
magnetization, magnon excitation spectra and spin-wave velocities are computed
as a function of the ratio between the second and first neighbours, J2/J1. We
find that near J2/J1 = 0.5, i.e., in the region where the classical spin
configuration changes from a Neel ordered phase to a spiral phase, the
staggered magnetization vanishes, suggesting the possibility of a quantum
disordered state. In this region, the quantum correction to the magnetization
is large but finite. This is in contrast to the frustrated Heisenberg model on
a square lattice, for which the quantum correction diverges logarithmically at
the transition from the Neel to the collinear phase. For large J2/J1, the model
becomes a set of chains with frustrated interchain coupling. For J2 > 4 J1, the
quantum correction to the magnetization, within LSW, becomes comparable to the
classical magnetization, suggesting the possibility of a quantum disordered
state. We show that, in this regime, quantum fluctuations are much larger than
for a set of weakly coupled chains with non-frustated interchain coupling.
