The massive Klein-Gordon field coupled to a harmonic oscillator at the boundary

We consider the massive Klein-Gordon field on the half line with and without a Robin boundary potential. The field is coupled at the boundary to a harmonic oscillator. We solve the system classically and observe the existence of classical boundary bound states in some regions of the parameter space. The system is then quantized, the quantum reflection matrix and reflection cross section are calculated. Resonances and Ramsauer-Townsend effects are observed in the cross section. The pole structure of the reflection matrix is discussed.