The free particle in spherical coordinates

loewenzahn · Dec 5, 2019

Hi!
I'm studying Shankar's Principle of quantum mechanics
I didn't get the last conclusion, can someone help me understand it, please. Where did the l over rho come from?

$Four-line derivation of the ladder operator step: rho R_{l+1} = d_l^dagger (rho R_l) = (-d/d rho + (l+1)/rho)(rho R_l), then R_{l+1} = (-d/d rho + l/rho) R_l, then rho^l (-d/d rho)(R_l / rho^l).$

strangerep · Dec 5, 2019

Expand the 2nd line. (And btw, if you still don't get it, show your attempt.)

The free particle in spherical coordinates

Discussion

Similar threads