There always exists at least one bound state for any negative attractive potential in one and two dimensions but not always in three dimensions

The claim specifically addresses the quantum mechanical behavior of bound states in 1D, 2D, and 3D under negative attractive potentials. Paper [0] directly supports the 1D and 2D portion of the claim, explicitly citing the well-known fact that arbitrarily weak attractive potentials possess a bound state in those dimensions. Paper [1] provides foundational conditions for bound states. The retrieved papers fully align with the standard physical principle stated in the claim.