Hydrogen Atom
AntiqueModules.HydrogenAtoms.HydrogenAtom — TypeH = HydrogenAtom(Z = 1, m_e = 1.0, a_0 = 1.0, E_h = 1.0, hbar = 1.0)
H = HydrogenAtom(Z = 1, mₑ = 1.0, a₀ = 1.0, Eₕ = 1.0, ħ = 1.0)Arguments
Z: …m_e(mₑ): …a_0(a₀): …E_h(Eₕ): …hbar(ħ): …
AntiqueModules.eigenvalue — Methodeigenvalue(model::HydrogenAtom; n::Int=1)\[E_n = -\frac{m_\mathrm{e} e^4 Z^2}{2n^2(4\pi\varepsilon_0)^2\hbar^2} = -\frac{Z^2}{2n^2} E_\mathrm{h},\]
where $E_\mathrm{h} = \frac{\hbar^2}{m_\mathrm{e}{a_0}^2} = \frac{e^2}{4\pi\varepsilon_0a_0} = \frac{m_\mathrm{e}e^4}{\left(4\pi\varepsilon_0\right)^2\hbar^2}$ is the Hartree energy, one of atomic unit. About atomic units, see section 3.9.2 of the IUPAC GreenBook. In other units, $E_\mathrm{h} = 27.211~386~245~988(53)~\mathrm{eV}$ from here.