  We study the Schrodinger-Newton system of equations with the addition of
gravitational field energy sourcing - such additional nonlinearity is to be
expected from a theory of gravity (like general relativity), and its appearance
in this simplified scalar setting (one of Einstein's precursors to general
relativity) leads to significant changes in the spectrum of the
self-gravitating theory. Using an iterative technique, we compare the mass
dependence of the ground state energies of both Schrodinger-Newton and the new,
self-sourced system and find that they are dramatically different. The Bohr
method approach from old quantization provides a qualitative description of the
difference, which comes from the additional nonlinearity introduced in the
self-sourced case. In addition to comparison of ground state energies, we
calculate the transition energy between the ground state and first excited
state to compare emission frequencies between Schrodinger-Newton and the
self-coupled scalar case.
