  We use the uniform light-cone gauge to derive an exact gauge-fixed Lagrangian
and light-cone Hamiltonian for the Green-Schwarz superstring in AdS5xS5. We
then quantize the theory perturbatively in the near plane-wave limit, and
compute the leading 1/J correction to a generic string state from the rank-1
subsectors. These investigations enable us to propose a new set of light-cone
Bethe equations for the quantum string. The equations have a simple form and
yield the correct spinning string and flat space limits. Finally, we clarify
the notion of closed sectors in string theory by proving the existence of
perturbative effective string Hamiltonians which are direct analogues of (all
loop) dilatation operators in the dual N=4 gauge theory.
