The rotational spectrum and the attractive delta-shell potential

The spectrum of the attractive delta-shell potential is investigated in the D-dimensional space (D >= 2). A compact expression for the eigenvalues is derived in the large coupling constant limit for odd dimensions D. With respect to the ground state energy, the spectrum is rotational, being proportional to L(L + D - 2), where L is the grand orbital momentum. Extension to even D is achieved on the grounds of the Hellmann-Feynman theorem. Simulating a delta-shell potential by a normalized Gaussian, we discuss finite range effects.