FIG.9:Sketch of (,0)as a function of 创 1-g+- -4G+g-ar号 →A=V停 (c)At r=a (d) -eaa-g-r号- -∫rt=4r{侣k+o可o- =()+（号-号+ =…=2a+b 4 Problem 3 Griffiths,page 14,Problem 1.5 17FIG. 9: Sketch of ψ(x, 0) as a function of x. (a) 1 = |A| 2 a 2 Z a 0 x 2 dx + |A| 2 (b − a) 2 Z b a (b − x) 2 dx = |A| 2    1 a 2 µ x 3 3 ¶a 0 + 1 (b − a) 2 Ã − (b − x) 3 3 !b a    = |A| 2 · a 3 + b − a 3 ¸ = |A| 2 b 3 ⇒ A = r 3 b (c) At x = a. (d) P = Z a 0 |ψ(x, 0)| 2 dx = |A| 2 a 2 Z a 0 x 2 dx = |A| 2 a 3 = a b    P = 1 if b = a √ P = 1/2 if b = 2a √ (e) hxi = Z x |ψ| 2 dx = |A| 2 ½ 1 a 2 Z a 0 x 3 dx + 1 (b − a) 2 Z b a x (b − x) 2 dx¾ = 3 b ( 1 a 2 µ x 4 4 ¶a 0 + 1 (b − a) 2 µ b 2 x 2 2 − 2b x 3 3 + x 4 4 ¶b a ) = · · · · · · = 2a + b 4 Problem 3 Griffiths, page 14, Problem 1.5 17