# Spectrum of an operator with a center of attraction [duplicate]

What can we qualitatively say about the spectrum of a Hamiltonian operator if the spectrum is not bounded from below but bounded from above?

e.g. $$\mathcal{H}=-\frac{d}{dx^2}-\frac{\lambda}{x^2}$$

This potential has a center of attraction at the origin.

• This inverse square potential is discussed in this Phys,SE post. – Qmechanic Nov 3 at 3:56