Angular functions of the hydrogen atom

After solving eqs. (2.1.12) and (2.1.13), it is found that, in order for functions to be meaningful, the separation constants mi and /3 must take the following values  

The integers l and mi are called azimuthal (or angular momentum) and magnetic quantum numbers, respectively. 

Moreover, the function ( ) depends on mi and hence is written as Pmt (p), while 0(9) depends on both l and mi and is written as 0i,mi(9)- Their product Y(9,4 ) thus also depends on both l and mi  

The Yim(6,(fi) functions are called spherical harmonics. They determine the angular character of the electronic wavefunction and will be of primary consideration in the treatment of directional bonding. 

Spherical harmonics, which describes the angular parts of the atomic orbitals, are labeled by their l values according to the scheme 

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