Physics · Quantum Mechanics (Perturbation Theory)
Consider a particle of mass m in a one-dimensional infinite potential well of width 2a, where V(x) = 0 for 0 ≤ x ≤ 2a, and V(x) = ∞ otherwise. The particle is subjected to a perturbation of the form W(x) = aεδ(x - a/2). The first-order energy shift for the n-th level is given by:
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- 1ε for n odd; ε/2 for n = 2, 6, 10...; 0 for n = 4, 8, 12...
- 2ε/4 for n odd; ε/2 for n = 2, 6, 10...; 0 for n = 4, 8, 12...✓
- 3ε/2 for n odd, ε for n even
- 4ε/2 for n odd, ε/4 for n even
Correct answer
ε/4 for n odd; ε/2 for n = 2, 6, 10...; 0 for n = 4, 8, 12...
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