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Exercises JRC2

From IFPA wiki
  1. Perform the integral giving the ground state of helium.
  2. Perform the coulomb and exchange integrals for the (1s)(2s) state of helium.
  3. Express the following operators in second quantisation for free bosons: [math]-i \sum_j^N\overrightarrow\nabla_j[/math], [math]\sum_i^N V(\overrightarrow r_i)[/math].
  4. Express the following operator in second quantisation for free fermions: [math]\sum_{i,j}{e^2\over |\overrightarrow r_i-\overrightarrow r_j|}\exp(-\mu|\overrightarrow r_i-\overrightarrow r_j|)[/math].
  5. How would you write the hamiltonian of the hydrogen atom in second quantisation?

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