Why the Integration Constant in the Schrödinger Equation is Set to L(L+1)?

[member 141513]

in the Schrödinger equation the integration constant in the angular wave
equation is set to L(L+1).
may i know why this is set ,what is the reason , thx!

 

[dextercioby]

Your question lacks naming the system for which the Schrödinger's equation is used.

If it was for the hydrogen atom, it may be worthy to know that the total angular momentum is a constant of motion and the H_{dummy particle} contains L^2 in its expression. When separating the spherical variables from the radial one, you're bumping into the spectral equation for L^2.

 

[jtbell]

I think you need to look at the details of the solution for the $\theta$ part of the Schrödinger equation in terms of associated Legendre polynomials.

 

[Meir Achuz]

The eigenvalues of the angular momentum operator L^2 are L(L+1).