Lecture 6

22 that was 1d but bulk objects metals semiconductors

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: le worked for 2 and 3 fermions. •  This Ime let’s focus on systems of many fermions in a 1D well (total # = N): E The total energy of the system is: n=N/2 EN/2 … ∞ E3 n=3 E2 n=2 E1 2 E1 + 2 E2 + 2 E3 + ... + 2 EN / 2 n=1  ­L/2 ! = 2" E j j =1 L/2 9 Many non ­interacIng fermions Now say that we have a LOT of parIcles…1023 = 100000000000000000000000 parIcles n E g = 2! E j j=1 E n=N/2 EN/2 E g = 2 E1 ! j E3 2 j=1 … ∞ n n=3 n = N/2 E2 n=2 E1 n=1  ­L/2 L/2 Eg N = En = E1n 2 = 1 n(n + 1)(2 n + 1) ! n 3 / 3 6 N3 13 Eg = 2 E1 = N E1 24 12 12 N E1 12 So the average energy of the electrons increases with the number of par9cles! 10 Fermi energy ! 2!2n2 •  Looking...
View Full Document

Ask a homework question - tutors are online