SM&M 7-5
a) E = hbar^2 Pi^2 / (2 m a^2) (n_x^2 + n_y^2 + n_z^2)
For graound state, n_x= n_y = n_z = 1
E = 3 hbar^2 c^2 Pi^2 / (2 m c^2 a^2)
= 3 (6.582E-16 eV sec 3E8 m/sec)^2 Pi^2 / (2 938.3e6 eV 2E-14^2)
= 1.54E6 eV = 1.54 MeV
b) First excited state
n_x = 2 n_y = 1 n_z =1
E = 6/3 E_0 = 2 E_0 = 3.08 MeV
Second excited state
n_x=2 n_y=2 n_z=1
E = 9/3 E_0 = 3 E_0 = 4.62 Mev
c) Degeneracy:
n_x n_y n_z
2 1 1
1 2 1 Three fold degeneracy for first excited state
1 1 2
2 2 1
2 1 2 Three fold degeneracy for second excited state
1 2 2