3. A useful recursion relationship for the associated Legendre Polynomials (solution to the equation) is cose...
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3. A useful recursion relationship for the associated Legendre Polynomials (solution to the equation) is cose p = 1 2J+1 Where: P = 1; Pº= cose; P = sine; P = (3cos²0-1); P = 3(1-cos²0) cose; P = (5cos³0 - 3cose) a) Show that the functions Po, P, P1, and Po obey the recursion relationship. b) m (0) = N₁ P Transitions between rotational states Jm and J'm' are governed by the relationship = ['m² (0) Aª Ym(6) sino de Where the dipole moment û is A = e(8 + 9 + 2) And I'm' have values different than Jm. When HTD #0 transitions occur. Use the recursion relationships to show rotational transitions are subject to the selection rule AJ = +1 for 2-dipole transitions. Hint: recall z = rcose. c) Show that P and P¹ are orthogonal. HTD= [0− [m] + 1) + (J + [m] 3. A useful recursion relationship for the associated Legendre Polynomials (solution to the equation) is cose p = 1 2J+1 Where: P = 1; Pº= cose; P = sine; P = (3cos²0-1); P = 3(1-cos²0) cose; P = (5cos³0 - 3cose) a) Show that the functions Po, P, P1, and Po obey the recursion relationship. b) m (0) = N₁ P Transitions between rotational states Jm and J'm' are governed by the relationship = ['m² (0) Aª Ym(6) sino de Where the dipole moment û is A = e(8 + 9 + 2) And I'm' have values different than Jm. When HTD #0 transitions occur. Use the recursion relationships to show rotational transitions are subject to the selection rule AJ = +1 for 2-dipole transitions. Hint: recall z = rcose. c) Show that P and P¹ are orthogonal. HTD= [0− [m] + 1) + (J + [m]
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