  We test the bootstrap approach for determining the spectrum of one
dimensional Hamiltonians, following the recent approach of Han, Hartnoll, and
Kruthoff. We focus on comparing the bootstrap method data to known analytical
predictions for the hydrogen atom and the harmonic oscillator. We resolve many
energy levels for each, and more levels are resolved as the size of the
matrices used to solve the problem increases. Using the bootstrap approach we
find the spectrum of the Coulomb and harmonic potentials converge exponentially
fast.
