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Exercise 3. Consider a particle with mass m in a two-dimensional infinite well of length L,...

Exercise 3. Consider a particle with mass m in a two-dimensional infinite well of length L, x, y ∈ [0, L]. There is a weak potential in the well given by

V (x, y) = V0L2δ(x − x0)δ(y − y0) .

  1. Evaluate the first order correction to the energy of the ground state.   
  2. Evaluate the first order corrections to the energy of the first excited states for x0 =y0 = L/4.
  3. For the first excited states, find the points (x0, y0) that do not remove the degeneracy to first order in V0.
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