3. Express the following operators in second quantisation for free bosons: $-i \sum_j^N\overrightarrow\nabla_j$, $\sum_i^N V(\overrightarrow r_i)$.
4. Express the following operator in second quantisation for free fermions: $\sum_{i,j}{e^2\over |\overrightarrow r_i-\overrightarrow r_j|}\exp(-\mu|\overrightarrow r_i-\overrightarrow r_j|)$.