/sci/ - Science & Math

>>15074123
i would be livid

>>14873788
theyre not always depicted like that.
youre right that the energy levels of an idealized "particle in a box" should go as [math]n^2[/math], but you should understand that it takes like 60 million assumptions before you arrive at thinking a cluster of atoms constitutes a nice box of potential. even just one (nonhydrogen) atom is already making assumptions when you go to solve its energy levels. slapping hundreds of (different) atoms together makes weird stuff happen. the band gap splitting in the first place is an example of this weird stuff.
all this to say, you cant take the particle in a box thing too seriously with sold-state physics. here, its mainly used to give plausibility when saying that "smaller particles have bigger gaps". spoiler: prefect crystals dont actually exist, and even if they did, perfect band gaps wouldnt exist either.