Bound states and scattering coefficients of the −aδ(x)+bδ′(x)−aδ(x)+bδ′(x) potential

We show that a one-dimensional Schrödinger equation in which the potential is a delta well plus a δ′δ′ interaction at the same point has a bound state, and we obtain the energy of this bound state in terms of the parameters. In addition, the expression of the reflection and transmission coefficients is also fully determined.