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Update HydrogenAtom.md #37
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ohno committed Apr 4, 2024
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# Hydrogen Atom

The hydrogen atom is the simplest 2-body Coulomb system.
The hydrogen atom is the simplest Coulomb 2-body system.

## Definitions

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```
and the Hamiltonian
```math
\hat{H} = - \frac{\hbar^2}{2\mu} \frac{\mathrm{d}^2}{\mathrm{d}r ^2} + V(r),
\hat{H} = - \frac{\hbar^2}{2m} \nabla^2 + V(r),
```
where $\mu=\left(\frac{1}{m_\mathrm{e}}+\frac{1}{m_\mathrm{p}}\right)^{-1}$ is the reduced mass of electron $\mathrm{e}$ and proton $\mathrm{p}$. $\mu = m_\mathrm{e}$ holds in the limit $m_\mathrm{p}\rightarrow\infty$. Parameters are specified with the following struct.
where $\mu=\left(\frac{1}{m_\mathrm{e}}+\frac{1}{m_\mathrm{p}}\right)^{-1}$ is the reduced mass of electron $\mathrm{e}$ and proton $\mathrm{p}$. $\mu = m_\mathrm{e}$ holds in the limit $m_\mathrm{p}\rightarrow\infty$. The potential includes only Coulomb interaction and it does not include fine or hyperfine interactions in this model. Parameters are specified with the following struct.

#### Parameters
```@docs; canonical=false
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