Hi! I'm studying the selection rules and the spectrum of one-electron atoms. In the textbook it is said: "It is convenient to introduce the spherical components of the vector [tex]\epsilon[/tex] which are given in terms of its Cartesian components by:(adsbygoogle = window.adsbygoogle || []).push({});

[tex]\epsilon_1=-\frac{1}{\sqrt2}(\epsilon_x+i\epsilon_y)[/tex]

[tex]\epsilon_0=\epsilon_z[/tex]

[tex]\epsilon_-1=-\frac{1}{\sqrt2}(\epsilon_x-i\epsilon_y)[/tex]

Can you please explain me these expressions?

I thought that

[tex]\epsilon_1=sin\theta cos\phi[/tex]

[tex]\epsilon_2=sin\theta sin\phi[/tex]

[tex]\epsilon_3=cos\theta[/tex]

so I can't understand the expressions given in the textbook

P.s. [tex]\epsilon[/tex] is the polarization vector, so it's a unit vector

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# Homework Help: Vectors in spherical coordinates

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