  Operators for simulating the scattering of two particles with spin are
constructed. Three methods are shown to give the consistent lattice operators
for PN, PV, VN and NN scattering, where P, V and N denote pseudoscalar meson,
vector meson and nucleon. The projection method leads to one or several
operators $O_{\Gamma,r,n}$ that transform according to a given irreducible
representation $\Gamma$ and row r. However, it gives little guidance on which
continuum quantum numbers of total J, spin S, orbital momentum L or
single-particle helicities $\lambda_{1,2}$ will be related with a given
operator. This is remedied with the helicity and partial-wave methods. There
first the operators with good continuum quantum numbers $(J,P,\lambda_{1,2})$
or $(J,L,S)$ are constructed and then subduced to the irreps $\Gamma$ of the
discrete lattice group. The results indicate which linear combinations
$O_{\Gamma,r,n}$ of various n have to be employed in the simulations in order
to enhance couplings to the states with desired continuum quantum numbers. The
total momentum of two hadrons is restricted to zero since parity P is a good
quantum number in this case.
