(a) Sandwich each of the six commutation relations in Equations 6.526.54 between (n''m'| and |nm) to obtain...

(a) Sandwich each of the six commutation relations in Equations 6.52–6.54 between (n'ℓ'm'| and |nℓm) to obtain relations between matrix elements of V̂. As an example, Equation 6.52 with the upper signs gives

(b) Using the results in Problem 6.23, show that the six expressions you wrote down in part (a) are satisfied by Equations 6.59–6.61.

Problem 6.23(a)

From Equation 6.64, show that the Clebsch–Gordan coefficients satisfy

Transcribed Image Text:

B (n'e' (m' - 1) | V+ |nelm) = A" (n'l'm' | V+ |ne (m + 1)).