Why do we have discrete energy levels in a quantum dot?

Answer 1

Actually, every finite system has discrete energy levels. They just more noticable in a quantum dot because it's so small.
particles in QM are described by a wave equation. The particle's energy is proportion to the frequency of vibration of the wave function. The different energy levels correspond to different harmonics of the particle confined to the dot.

Answer 2

because it is too small to create giant enrgy levels unless bashing together is possible(either im so right or so wrong... ps i tried)