13 Jun 2026

Example

code, example

some example

## The equation to solve

$$
\frac{1}{2m} p^{2} \psi(\mathbf{p})
- \frac{Z e^{2}}{2\pi^{2}\hbar}
\int
\frac{\psi(\mathbf{p}')\,(\mathrm{d}\mathbf{p}')}
{|\mathbf{p}-\mathbf{p}'|^{2}}
= E\,\psi(\mathbf{p}),
$$

where $(\mathrm{d}\mathbf{p}’) = \mathrm{d}p_x’\,\mathrm{d}p_y’\,\mathrm{d}p_z’$ denotes the volume element in momentum space.
We denote the discrete spectrum by $E$ and introduce the mean quadratic momentum

\[p_{0} = \sqrt{-2mE}. \tag{2}\]