The BFSS exclusion of positive-energy normalizable states in the relative SU(2) model

Theorem 1.1: the relative $\mathrm{SU}(2)$ BFSS Hamiltonian has infinitely many positive eigenvalues $E_j\to\infty$ with square-integrable eigenvectors, so $\sigma_p(H)\cap(0,\infty)$ is infinite. This contradicts, for this exact operator at $N=2$, the BFSS paper's sentence excluding other normalizable bound states. It concerns only $N=2$, says nothing about $N\ge3$, and does not bear on the zero-energy state (the companion entry) or on large-$N$ matrix theory.

Theorem 1.1: the relative $\mathrm{SU}(2)$ BFSS Hamiltonian has infinitely many positive eigenvalues $E_j\to\infty$ with square-integrable eigenvectors, so $\sigma_p(H)\cap(0,\infty)$ is infinite. This contradicts, for this exact operator at $N=2$, the BFSS paper's sentence excluding other normalizable bound states. It concerns only $N=2$, says nothing about $N\ge3$, and does not bear on the zero-energy state (the companion entry) or on large-$N$ matrix theory.