Sr2Cu3O4Cl2 is an antiferromagnet consisting of weakly coupled CuO planes w
hich comprise two weakly interacting antiferromagnetic subsystems I and II
which order at respective temperatures T-I approximate to 390 K and T-II ap
proximate to 40 K. Except asymptotically near the ordering temperature, the
se systems are good representations of the two-dimensional quantum spin-1/2
Heisenberg model. For T< T-II there are four low-energy modes at zero wave
vector, three of whose energies are dominated by quantum fluctuations. For
T-II< T< T-I there are two low-energy modes. The mode with lower energy is
dominated by quantum fluctuations. Our calculations of the energies of the
se modes (including dispersion for wave vectors perpendicular to the CuO pl
anes) agree extremely well with the experimental results of inelastic neutr
on scattering (in the accompanying paper) and for modes in the sub-meV rang
e observed by electron spin resonance. The parameters needed to describe qu
antum fluctuations are either calculated here or are taken from the literat
ure. These results show that we have a reasonable qualitative understanding
of the band structure of the lamellar cuprates needed to calculate the ani
sotropic exchange constants used here.