a) The enngy eigenstates of puntill in 10 hox: Since the box is symmetrical (-aia) K= (2n-1) a za Ena th² (20) 272 2m 40² For 2D box Enn = t 2 {(2,-1) + (21,-1). ²] 8ma² Using m= 0.07749. 108 x 10-31 kg a = 3x10-9 m E , = 0.269 eV E12 = EU = 1.347 eV (doubly degeneute) E22 = 2.424 eV 2.424 eV 1,347 ev 112) and 12, 1) Energy 0.269 V 111)
(b) The eigenstates: 20 . Thin, = A con f(24..) cos [com, -1) ay] Chí nélğının) = A dd / dy con (kin) cookiy) y cos(k, h) cos (key) 22 / dn cos (Kín) cos (K, P) ( dy y cos (ky) cos (keiz) The first punti da cos CR, 2) cos Ckin) cos (Kintk, R) & cos(kin-kin) / de cos[(kirk, n1 + 1 du cost cki-k,) ~] I sin Ckitk,) a t a 1 1 2 kitki sin (ki-k)n 2 Kitk) => castssim [ .(20/+n)-2)] a Mix) Sim ( ro ( 2 (0ani) -2) 11a for his to be O, k, k, il-n, ini
Тво и от (к. 2) (0) (к) zens tk) in La Cuens en ) 9-) Det mesy-to ein (2 -) -2)] oly working in Long (2 cus tn)-2)] + szkenne) - sin ( m ( 2 Chý - 1₂) -2)] H -- Bin - - - K gob to o for nyt " gos to some finite value for nitu selection will for transitions: Therefore the n = n and net ni