Consider a spherical tensor of rank 1 (that is, a vector)

Using the expression for d(J=l) given in Problem 3.26, evaluate

and show that your results are just what you expect from the transformation properties of V_x,y,z under rotations about the y-axis.

Data from problem 3.26:

Consider a system with j = 1. Explicitly write

in 3 x 3 matrix form.

Show that for j = 1 only, it is legitimate to replace e^-iJyβ/h̄ by

Using (b), prove

Transcribed Image Text:

V +1=F V x ±i Vy √2 V() = V₂.