  We formulate a new quasi-Hermitian delta-shell pseudopotential for higher
partial wave scattering, and show that any such potential must have an
energy-dependent regularization. The quasi-Hermiticity of the Hamiltonian leads
to a complete set of biorthogonal wave functions that can be used as a basis to
expand and diagonalize other two-body Hamiltonians. We demonstrate this
procedure for the case of ultracold atoms in a polarization-gradient optical
lattice, interacting pairwise when two atoms are transported together from
separated lattice sites. Here the pseudopotential depends explicitly on the
trapping potential. Additionally, we calculate the location of trap-induced
resonances for higher partial waves, which occur when a molecular eigenstate is
shifted to resonance with a trap eigenstate. We verify the accuracy of the
pseudopotential approach using a toy model in which a square well acts as the
true interaction potential, and see excellent agreement.
