1. How many electrons can be trapped at the heterojunction described by the triangular potential in the earlier problem with only the lowest subband occupied? Roughly how cold must the sample be for thermal occupation of higher subbands to be negligible?

2. A quantum dot is confined in two dimensions by a parabolic potential that rises 50 meV over a radius of 100 nm. Confinement is much stronger in the third dimension, and it can be assumed that all electrons remain in the lowest state for this dimension. How many states are occupied if the Fermi level lies 12 meV above the minimum? How would the results differ if the dot were instead modelled with a hard wall at 50 nm radius?