  We apply the eigenvectors from a variational analysis in lattice QCD to
successfully extract the wave function of the Roper state, and a higher mass
P_11 state of the nucleon. We use the 2+1 flavour 32^3x64 PACS-CS
configurations at a near physical pion mass of 156 MeV. We find that both
states exhibit a structure consistent with a constituent quark model. The Roper
d-quark wave function contains a single node consistent with a 2S state, and
the third state wave function contains two, consistent with a 3S state. A
detailed comparison with constituent quark model wave functions is carried out,
obtained from a Coulomb plus ramp potential. These results validate the
approach of accessing these states by constructing a variational basis composed
of different levels of fermion source and sink smearing. Furthermore,
significant finite volume effects are apparent for these excited states which
mix with multi-particle states, driving their masses away from physical values
and enabling the extraction of resonance parameters from lattice QCD
simulations.
