It is well known that Schrödinger operator with degenerate kinetic energies may support infinitely many weakly coupled bound states. Hainzl and Seiringer proved that the eigenvalues of $|p^2-1|-\lambda V$ are exponentially small as the coupling constant $\lambda$ tends to zero, and they connected the problem to an effective operator on the sphere. This holds essentially under the assumption that the potential is integrable. In this talk I will show that one can relax this condition considerably and cover a much larger class of potentials. This is joint work with Konstantin Merz.

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