Exercises JRC2
From IFPA wiki
- Perform the integral giving the ground state of helium.
- Perform the coulomb and exchange integrals for the (1s)(2s) state of helium.
- Express the following operators in second quantisation for free bosons: [math]\displaystyle{ -i \sum_j^N\overrightarrow\nabla_j }[/math], [math]\displaystyle{ \sum_i^N V(\overrightarrow r_i) }[/math].
- Express the following operator in second quantisation for free fermions: [math]\displaystyle{ \sum_{i,j}{e^2\over |\overrightarrow r_i-\overrightarrow r_j|}\exp(-\mu|\overrightarrow r_i-\overrightarrow r_j|) }[/math].
- How would you write the hamiltonian of the hydrogen atom in second quantisation?