- Exercise Matrix Elements Of A Scalar Operator 25 10 Point Graded Recall The Angular Momentum Identities Juli M 1 1 (49.6 KiB) Viewed 37 times
Exercise: Matrix elements of a scalar operator -25 10 point (graded) Recall the angular momentum identities Juli, m) = 16+1) - m(m+1) l), m #1), JJ_ = JP - J} + HJ. Consider a scalar operator , meaning J., Ô) = 0, and define f(,m) = (j, môj, m). Evaluate (j, mÔJ J-1), m) directly. Assume m-j. • Evaluate (j, mÔJ J-\j, m) by noticing it is equal to (j, m|JA0J-\j, m) because Ô is a scalar operator. What do you conclude from the two evaluations? . of 0,m) = -f(,m-1) of (m) = f ,m-1) of G, m) = 2f (,m+1) o fa,m) = -2fG, m+1) of, m) = f (+1, m - 1) o f(m) = f(-1, m +1)