The transmission coefficient and total cross section as functions of energy are obtained for scattering of particles by a double δ-function potential in one dimension. This example may be useful for the discussion of resonance scattering in an introductory quantum mechanics course. (AIP)
The energy and parity eigenstates for quadrupolar, triple δ-function potential are analysed. Using the analytical solutions in specific domains, simple expressions are obtained for even- and odd-parity bound-state energies. The Heisenberg uncertainty product is observed to have a minimum for a specific strength of the potential. The scattering states have a transmission resonance for some energies, and the poles of the transmission coefficients correspond to bound-state energies. These features are of considerable pedagogical interest in the understanding of quantum-mechanical properties of bound and scattering states, for graduate and general physicists.