Hyperspherical δ-δ′ potentials

The spherically symmetric potential aδ(r−r0)+bδ′(r−r0) is generalised for the d-dimensional space as a characterisation of a unique selfadjoint extension of the free Hamiltonian. For this extension of the Dirac delta, the spectrum of negative, zero and positive energy states is studied in d≥2, providing numerical results for the expectation value of the radius as a function of the free parameters of the potential. Remarkably, only if d=2 the δ-δ′ potential for arbitrary a>0 admits a bound state with zero angular momentum.