Formulas for Angular Momentumwhere h is Planck's constant. Since this is quantum mechanics, of course, only certain discrete amounts of angular momentum are allowed; that's why l has to be an integer. The quantum number m refers to the projection of the angular momentum in a direction of your choice, conventionally called the z direction. L_{z}, the component of angular momentum in the z direction, is given by the formula
For example, let's say you choose the z direction to be vertical. The pink
dotted arrow in this picture represents the vector L. The solid blue
and red arrows are its horizontal and vertical components; the length of the
vertical red arrow is L_{z}.

