Question

for sco The wave function of a particle is given as V000) = { 0, La expr-c) for x7o. Where a es constant a determine a so that this wave function is normalized ii) Sketch probability density il calculate the expectation value of ac in calculate uncertainty 4x

this question is worth 20 marks so please give detail and explain clearly in good English how to answer the questions
will reward with like :)

Answer 1

O 0 The wave function of a particle is given as Y) = a exp (-x) for no for xro where a = constant. We know normalization condition as eta 4*624() dre = 1 where 4*) - complex Conjugate of Y(x) [° 4*CN) 4 (3) dx + 07 (YOM) Y () dx = 1 OY, O + az e-2a de = 1 OY ar si e-20 dx = 1 OY a - 2x e 1 2 0 or OY a = √2 constant. a> [0+'j] = 1 rmis is the value of normalization Now wave function become 4(x) = sizex for 4,0 lo for alo

0 Probability Density f(x) = 4* (x) 4 (2) 140214 ar 8 (2) 2 or SEND = 22-23 ploted in Desmos. anis is graph

vo 12:31 AM 0.2KB/s LTE fall 75 8 101 6 4 2 -2 O 2 4 6 --2 .-4 -6 a

Now expectation value of a La) as yra) ã YOu) dx tal - 22 2e 2 da in-ax xe de a n! 2 -2x dx anti 2 2 xe So 2 2 x 1! [:n na 1 Here 22 Q = ļ

(iv (fo Now (52) 2 102 row dix "zxe de - 2x de 22 xe = 2 x 23 2! 3 2 4 8 2 2 . An 2 - √ 2 - 1 SA muis is the uncertcinity ox. 4 -- 4X 2