Question

Part A A three-dimensional potential well has potential Uo = 0 in the region 0 < x <L, 0<y<L, and 0 <z<2L and infinite potential otherwise. The ground state energy of a particle in the well is E. What is the energy of the first excited state, and what is the degeneracy of that state? 3Eo, triple degeneracy 2Eo, single degeneracy 2Eo, double degeneracy (7/3)Eo, double degeneracy (4/3)Eo, single degeneracy Submit Request Answer

Answer 1

Aus- 021८L O.<YLL, OcZcal The energy levels of the particle is given by Enginn h² nx Nz 8m Z (24) Enry, Ayiniz ny + + 2 2 nx h² om N + + ² 42 크 Na 1, 2, 3, ny 1,2,3, nz ground state corresponds na ny = 72 = 1 1, 2, 3, بلبرگ Eo 8m4

E ime² And the first excited state would collespond to (le 2, ny = M₂ = 1 ) or (x=1; M., 22 , 12 ) or (1) ny = 1, n₂ =2) encigy of the first excited state for 2, 1, 1) = he 14 T 4 + 1 + + h² 21 8 m2 Similarly E21 ha 41+++ 8m2 4 (22) Erit €1,2 n 3 h? 17 1+1.). 8m² 8m2 14 2

ماينرار 38m2 As 6,2 < Ery and E,,,2 E, 1,2 < Ezt hence the energy of the fisst excited excited state Also 3n² 6, 4 n² 9 Ime 1/ Eo = the energy of the first excited state 4/ la Also as no other state has this energy so the so the first excite state in singly degenerate.