The bound eigenstates of an electron inside a pair of quantum dots embedded on an infinite quantum wire are examined using the method of particular solutions. The eigenstates of a two-electron system in the same structure are examined perturbatively using wavefunction expansions for the one-electron eigenstates. The stability of the two-electron eigenstates is evaluated and compared with other theoretical results. It is found that stable bound states in the continuum exist for two electrons confined to this geometry
