Consider an electron in the hydrogen atom that was occupying the following quantum state combination of position and spin: 2 V (r, 0, ¢) = R12 Y°(0,¢)x +Y?(0,¢)x- 3 (3.1) Where R21 (r) is the radial function of the hidrogen atom with: n=2,1=1 and Y" are spherical harmonics and x+ = (6), x- = () are spinors a) What values and with what probability do you find the squared angular mo- mentum (j?)..J = L+S b) find the values and probability of the proyection of [J] in the z-direction, J,

Consider an electron in the hydrogen atom that was occupying the following quantum state combination of position and spin: 2 V (r, 0, ¢) = R12 Y°(0,¢)x +Y?(0,¢)x- 3 (3.1) Where R21 (r) is the radial function of the hidrogen atom with: n=2,1=1 and Y" are spherical harmonics and x+ = (6), x- = () are spinors a) What values and with what probability do you find the squared angular mo- mentum (j?)..J = L+S b) find the values and probability of the proyection of [J] in the z-direction, J,