What is the corresponding letter and orbital for L=1?

For the angular momentum quantum number ( L = 1 ), the corresponding letter that represents the shape of the orbital is ( P ). In quantum mechanics, the letters used to designate the angular momentum quantum numbers are as follows: ( S ) for ( L = 0 ), ( P ) for ( L = 1 ), ( D ) for ( L = 2 ), ( F ) for ( L = 3 ), and ( G ) for ( L = 4 ).

The designation ( P ) indicates p-orbitals, which have a distinctive dumbbell shape and are oriented along specific axes in three-dimensional space. The p-orbitals can hold a total of six electrons, with three different orientations (( m_L = -1, 0, +1 )).

In terms of symmetry labels such as ( T_{1g} ), ( T_{2g} ), ( A_{1g} ), etc., these pertain to the specific symmetry properties of electronic configurations in crystal field theory and group theory contexts, often used for determining energy levels in transition metal complexes. However, they are not a direct correspondence to the angular momentum quantum number (