Question

2.33. Evaluate (x), (Px), A.x, APx, and Ax Apr for the normalized wave function { (x)= sin 0<x</ 0 elsewhere In the next chapter we will see that this wave function is the ground-state wave function for a particle confined in the potential cnergy well 0 V(x) = { 0 <r <L elsewhere

Answer 1

8. Given wave function_V(x)= I sinar (KAL L O elsewhere • The_expectation value of x (K) dx L on <r) = [५.xxx.pter) -४ ( | - OS 2TY) L 2 fxsin (axy dx 2 L 2 -- 1 70 R) 1x dx - + X COS(24) dn COSH 6 where T K cos भारत -O I= x sin 2 L 25 sis (re) Conta) = Firedra 2-X 2 ले / 12 का) 1248 50 (x) • <b> = *(x)(x) dx * ए - xe 쭌 'x कि IL or L 지 L COSTK L + (२) -A Kh)= - 27 SHARE) aas /)- L L क) Likr fsimparar (क) They = (-1) 2 K । ory) hx L (뷔 27 र) 20

(x) L [{x)_x2 ulix) dre x sth (m) de 은하에 2. 05. PT 에 ~ 19 0 x2) feite - frezen (23de хр 나 0 . 1) - - 구 where A = h cos (271or L, II 0 L L A. x² siñaxi L 2 x sin (27x (P 4x 2 0 - ASMO ㅉ 0 A -L OI) t oldn sinax ㅈ ㅈ 0 00 (r 為 2 . 옴 II sin fax L LL x) = •) 의 A FAI) -> - I - (-) () Fin() 4) - ( sine dk = 은 2) + 이 사장 (4) ex = | Ixe) - xy 개마 Cos2dc LlLiz ㅉ L ㅉ L ond 된 SG 간 Drobe 뜨 112 X 12