  We present a detailed theoretical analysis of the electronic structure of
$c$-plane InGaN/GaN quantum wells with indium contents varying between 10\% and
25\%. The electronic structure of the quantum wells is treated by means of an
atomistic tight-binding model, accounting for variations in strain and built-in
field due to random alloy fluctuations. Our analysis reveals strong
localisation effects in the hole states. These effects are found not only in
the ground states, but also the excited states. We conclude that localisation
effects persist to of order 100~meV into the valence band, for as little as
10\% indium in the quantum well, giving rise to a significant density of
localised states. We find, from an examination of the modulus overlap of the
wave functions, that the hole states can be divided into three regimes of
localisation. Our results also show that localisation effects due to random
alloy fluctuations are far less pronounced for electron states. However, the
combination of electrostatic built-in field, alloy fluctuations and structural
inhomogeneities, such as well-width fluctuations, can nevertheless lead to
significant localisation effects in the electron states, especially at higher
indium contents. Overall, our results are indicative of individually localised
electron and hole states, consistent with the experimentally proposed
explanation of time-dependent photoluminescence results in $c$-plane InGaN/GaN
QWs.
