Question

1/2) confined in a one-dimensional rigid box (an infinite Imagine an electron (spin square well). What are the degeneracies of its energy levels? Make a sketch of the lowest few levels, showing their occupancy for the lowest state of six electrons confined in the same box. Ignore the Coulomb repulsion among the electrons. (6 points) S =

Answer 1

Answev pazhde ID box finfimike squane well) When ionfíned in a A Wallpared wall may only be faund here The boundary condilaei. the pantidevaashrat the beumday 4klo)- 0_& YKCi) z0 is that wasefuncien foy The tume independent Stanadages aualeza fo paih'clof man mmoving encagayEis. a duicion with ai 1n Vix) Y(x) : E4(x) Vk) = polentsal inegn x1 wavefamcbon wrthum wele, hunce Foy this case 2 YV Selutien is x) = A &mkx t B os Kx. e_Bewndary ondleón On Yix ) = Asin (kx)

Solung faA (x)= 0, huma uhem x- Sm Xo them X 8n2mEL nz2,3,- 2 From this E 2. 2 m2 812 mt 2 E. 2 Since n23- ene-dumenaenal case) degneray(zera dageenay 2

En n2 Note Enesgy lewel spacang mucases with Now fer eletrons tee is and adoun Heme huo elections cuspy ashate Addeag 4tauhug fon cam Llerlions X of fris syptemwl he f32 h2 12 h2 22 h 2X 2. 2 28 2 m1 2