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Two vector operators aimed at shifting angular momentum quantum number l inspherical harmonics |lm>, primarily proposed by Prof. X. L. Ka in 2001, arefurther studied. For a given magnetic quantum number m, specific states |lm> inspherical harmonics with the lowest angular momentum quantum numbers l areobtained and the state with minimum angular momentum quantum number in wholeset of the spherical harmonics is |0,0>. How to use these states to generatewhole set of spherical harmonics is illustrated.

Raising and lowering operators for angular momentum quantum numbers l in spherical harmonics