13.8. Our goal is to establish (13.60), which, with the aid of (13.59), can be put...

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13.8. Our goal is to establish (13.60), which, with the aid of (13.59), can be put in the form eikr cos i√47 (21+1) j₁(kr)Y₁,0(0) = (b) Use the fact that 1=0 (a) Explain why the expansion of the plane wave must be of the form eikr cos-c₁ j(kr)Y₁,0(0) 1=0 12, 0) = (see Problem 9.18) to show (21)! (4) [1, Z) cijiler) = √(211 / 42 v ²1 {[1²0 (180 - } 20 cot 0. a ap eikr cos 8 d' d (cos 9)¹ /(21)! [ as y, [(-1)'elle sin e- Υ eikr cos 9 where the last step follows from the explicit form (9.142) for the raising operator in position space. (c) Use the explicit form (9.146) for Y₁(0, 0) to express this result in the form cji(kr) = (ikr)- 24/1 47 √(21)! (21 + 1)! ds (Y/(0.4) Peikr cos 6 (d) Finally, isolate c, by evaluating this expression as r → 0. Hint: For small r, ji(kr) behaves as (kr)/(21+ 1)!!, where (21+ 1)!!= (21 + 1) (21-1)... 5. 3.1. 13.8. Our goal is to establish (13.60), which, with the aid of (13.59), can be put in the form eikr cos i√47 (21+1) j₁(kr)Y₁,0(0) = (b) Use the fact that 1=0 (a) Explain why the expansion of the plane wave must be of the form eikr cos-c₁ j(kr)Y₁,0(0) 1=0 12, 0) = (see Problem 9.18) to show (21)! (4) [1, Z) cijiler) = √(211 / 42 v ²1 {[1²0 (180 - } 20 cot 0. a ap eikr cos 8 d' d (cos 9)¹ /(21)! [ as y, [(-1)'elle sin e- Υ eikr cos 9 where the last step follows from the explicit form (9.142) for the raising operator in position space. (c) Use the explicit form (9.146) for Y₁(0, 0) to express this result in the form cji(kr) = (ikr)- 24/1 47 √(21)! (21 + 1)! ds (Y/(0.4) Peikr cos 6 (d) Finally, isolate c, by evaluating this expression as r → 0. Hint: For small r, ji(kr) behaves as (kr)/(21+ 1)!!, where (21+ 1)!!= (21 + 1) (21-1)... 5. 3.1.

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free particles moving described by the The when the the wave L0 Yk ekz wave function of a ... View the full answer