## Developing a Hartree-Fock program, additional considerations

Note that \( \langle \alpha\vert\hat{h}_0\vert\beta \rangle \) denotes the
matrix elements of the one-body part of the starting hamiltonian. For
self-bound nuclei \( \langle \alpha\vert\hat{h}_0\vert\beta \rangle \) is the
kinetic energy, whereas for neutron drops, \( \langle \alpha \vert \hat{h}_0 \vert \beta \rangle \) represents the harmonic oscillator hamiltonian since
the system is confined in a harmonic trap. If we are working in a
harmonic oscillator basis with the same \( \omega \) as the trapping
potential, then \( \langle \alpha\vert\hat{h}_0 \vert \beta \rangle \) is
diagonal.