Finding bound state and scattering matrix of Hamiltonian

[jojo2255]

Given that the Hamiltonian is H = P^2/(2m) + aδ(X − x(naught)) + bδ(X + x(naught), where x(naught) is a positive number. Find the conditions for bound states to exist and calculate their energies. Find the scattering matrix for arbitrary values of a and b.

Can someone help me solve this please.

 

[MisterX]

This is similar to the double delta potential, except with different scaling on each delta. I think if you look at Griffith's QM book you should techniques for single or double delta potentials. I think you can apply a similar technique here.
In the regions where there is no delta, the solution will be a exponential wave. To this apply the boundary conditions that the potential creates between the different regions. The S matrix in one dimension is a relation between the regions on either side.https://en.wikipedia.org/wiki/S-matrix#S-matrix_in_one-dimensional_quantum_mechanics