  We have theoretically studied exciton states and photoluminescence spectra of
strained wurtzite AlGaN/GaN quantum-well heterostructures. The electron and
hole energy spectra are obtained by numerically solving the Schr\"odinger
equation, both for a single-band Hamiltonian and for a non-symmetrical 6-band
Hamiltonian. The deformation potential and spin-orbit interaction are taken
into account. For increasing built-in field, generated by the piezoelectric
polarization and by the spontaneous polarization, the energy of size
quantization rises and the number of size quantized electron and hole levels in
a quantum well decreases. The exciton energy spectrum is obtained using
electron and hole wave functions and two-dimensional Coulomb wave functions as
a basis. We have calculated the exciton oscillator strengths and identified the
exciton states active in optical absorption. For different values of the Al
content x, a quantitative interpretation, in a good agreement with experiment,
is provided for (i) the red shift of the zero-phonon photoluminescence peaks
for increasing the quantum-well width, (ii) the relative intensities of the
zero-phonon and one-phonon photoluminescence peaks, found within the
non-adiabatic approach, and (iii) the values of the photoluminescence decay
time as a function of the quantum-well width.
