  Nanoscale inhomogeneity seems to be a central feature of the d-wave
superconductivity in the cuprates. Such a feature can strongly affect the local
density of states (LDOS) and the spectral weight functions. Within the
Bogoliubov-de Gennes formalism we examine various inhomogeneous configurations
of the superconducting order parameter to see which ones better agree with the
experimental data. Nanoscale large amplitude oscillations in the order
parameter seem to fit the LDOS data for the underdoped cuprates. The
one-particle spectral function for a general inhomogeneous configuration
exhibits a coherent peak in the nodal direction. In contrast, the spectral
function in the antinodal region is easily rendered incoherent by the
inhomogeneity. This throws new light on the dichotomy between the nodal and
antinodal quasiparticles in the underdoped cuprates.
