The wave functions that specify the state of the electron depend not only on the x,y,z coordinates but also on the spin of the electron. The complete wave function is constructed by multiplying the spatial (orbital) part by the corresponding spin function. When introducing the spin, the doubling of the hydrogenoid quantum states is produced, without there being a change in energy. Thus, the first hydrogenoid energy level (ground state) will be formed by two degenerate quantum states, whose wave functions are: \begin{eqnarray} \psi_{1s}(x,y,z)\cdot\alpha(m_s) \\ \psi_{1s}(x,y,z)\cdot\beta(m_s) \end{eqnarray} The degeneracy of the energy levels of the hydrogen atom goes from $n^2$ to $2n^2$.

# Helioid atoms | Quantum Mechanics

## Spin in the hydrogen atom

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- Written by: Germán Fernández
- Category: Helioid atoms | Quantum mechanics
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