Abstract
In this chapter we study the Stark effect and the Zeeman effect on atoms, and in particular on the Hydrogen atom.
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- 1.
The Wigner-Eckart theorem states that for any vector operator \({\hat{\mathbf{V}}}= ({\hat{V}}_1,{\hat{V}}_2,{\hat{V}}_3)\) such that \([{\hat{J}}_i,{\hat{V}}_j]=i\hbar \epsilon _{ijk} {\hat{V}}_k\) holds the identity
$$\begin{aligned} \hbar ^2 j(j+1) \, \langle n,l,s,j,m_j |{\hat{\mathbf{V}}}|n,l,s,j,m_j\rangle = \langle n,l,s,j,m_j |({\hat{\mathbf{V}}}\cdot {\hat{\mathbf{J}}})\, {\hat{\mathbf{J}}} |n,l,s,j,m_j\rangle \; . \end{aligned}$$In our case \({\hat{\mathbf{V}}}={\hat{\mathbf{S}}}\) and we have considered the z component only.
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Salasnich, L. (2017). Energy Splitting and Shift Due to External Fields. In: Quantum Physics of Light and Matter . UNITEXT for Physics. Springer, Cham. https://doi.org/10.1007/978-3-319-52998-1_5
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DOI: https://doi.org/10.1007/978-3-319-52998-1_5
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