Q14(a). Degeneracy in a cubic box; states with E = 101h²/8mL²
What is degeneracy? Illustrate with the cubic box of length L. How many eigenstates are there with energy equal to 101h²/8mL²?
Answer in brief
Degeneracy: different eigenstates with the same energy. For E = 101h²/8mL², nx² + ny² + nz² = 101 has three sets, {1,6,8}, {2,4,9}, {4,6,7}, each with 6 orderings: 18 eigenstates.
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Coversdegeneracyparticle in a cubic boxaccidental degeneracyeigenstatesthree-dimensional box
All parts of Question 14
- 14(a) Degeneracy in a cubic box; states with E = 101h²/8mL²10 marks
- 14(b) Particle in a box with sides a, b, c: ψ, E and the Laplacian10 marks