  We employ the technique of perturbative analytic null bootstrap to obtain the
energy eigenvalues and ladder operators of the sextic anharmonic oscillator up
to second order in the coupling. We confirm our results by deriving the same
from traditional perturbation theory. We further perform the bootstrap approach
on non-Hermitian PT symmetric Hamiltonians, focusing on the shifted harmonic
oscillator and the celebrated cubic anharmonic oscillator.
