  We develop strong-coupling series expansion methods to study two-particle
spectra of quantum lattice models. At the heart of the method lies the
calculation of an effective Hamiltonian in the two-particle subspace. We
explicitly consider an orthogonality transformation to generate this block
diagonalization, and find that maintaining orthogonality is crucial for systems
where the ground state and the two-particle subspace are characterized by
identical quantum numbers. We discuss the solution of the two-particle
Schr\"odinger equation by using a finite lattice approach in coordinate space
or by an integral equation in momentum space. These methods allow us to
precisely determine the low-lying excitation spectra of the models at hand,
including all two-particle bound/antibound states. Further, we discuss how to
generate series expansions for the dispersions of the bound/antibound states.
These allow us to employ series extrapolation techniques, whereby binding
energies can be determined even when the expansion parameters are not small. We
apply the method to the (1+1)D transverse Ising model and the two-leg
spin-$\case 1/2$ Heisenberg ladder. For the latter model, we also calculate the
coherence lengths and determine the critical properties where bound states
merge with the two-particle continuum.
