For a particle in a 3dimensional cubic box the energy can be

For a particle in a 3-dimensional cubic box, the energy can be calculated as a funcitoon of 3 three quantum numbers:

Which two sets are degenerate (are equal in energy)?

4. For a particle in a 3-dimensional cubic box, the energy can be calculated as a function 3 three quantum numbers. En rMy,n~ 8m22 (he + 72i) + n2) Given different sets of quantum numbers, quantum numbers: Enrnu Set I Set2 2 Set3 2l Set4 I 2 3 Set5 2 22 which two sets are degenerate (are equal in energy)?

Solution

Set 2 and 3 are degenrate as they have the same value of L and n_x² + n_y^{2 +}n_z²

For set 2

n_x² + n_y^{2 +}n_z²   = 4+1+1 =6

For Set 3

n_x² + n_y^{2 +}n_z² = 1 + 4+1 =6

Hence both will have same energy and hence will be degenerate