V = Infinity for x<0 V = 0 for 0<= x < a V = +V0 for x => aAfter sketching the potential, draw the wave function for the ground state and for the first and second excited states.
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
a) |L| ~ l hbar --> l ~ L/hbar = 4.83E31/1.055E-34 = 4.58E65 b) fractional change = 1/4.85E65 = 2.2E-66 !!!