# Why is separation constant l(l+1) instead of +-l^2?

While separating variables in the Schrodinger Equation for hydrogen atom, why are we taking separation constant to be l(l+1) instead of just l^2 or -l^2, is it just to make the angular equation in the form of Associated Legendre Equation or is there a deeper meaning to it?

Orodruin
Staff Emeritus
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Because those are the eigenvalues to the angular operator. You do not ”choose” the eigenvalues, they are what they are based on the differential equation and boundary conditions. In the case of the angular part of the Laplace operator, the eigenfunctions have those eigenvalues.

vanhees71
strangerep