where the superscript (1) signifies that the defined quantities are the components of a spherical tensor operator of rank k = 1 (which explains the factor √ 2 as well) and the subscripts 0, ±1 are referred to as q in formulas below, are given by ⟨ j ′ m ′ | K 0 ( 1 ) | j m ⟩ = ⟨ j ′ m ′ k = 1 q = 0 | j m ⟩ ⟨ j ‖ K ( 1 ) ‖ j ′ ⟩ , ⟨ j ′ m ′ | K ± ± 1 ( 1 ) | j m ⟩ = ⟨ j ′ m ′ k = 1 q = ± ± 1 | j m ⟩ ⟨ j ‖ K ( 1 ) ‖ j ′ ⟩ .