Question

I have found answers to part a and b and just really need help with part c! and the extra if you have time.

5. Wave mechanics: (10 points) Suppose to have the following wave function (-oo 〈 x 〈 +00) r2 a for constants A and a a) Determine A, by normalize V(x). b) Use Ψ(x) to find the expectation values (a), (z2)), and σ,-V(z2,-(z c) Find the momentum space wave function (p), and check that it is normalized. EXTRA POINTS d) Use Ψ(p) to find the expectation values (p), (p2), and σ,- e) Check the Heisenberg uncertanty principle for this state. V(p2)-(P)

A=$sqrt(\frac{2a^{3}}{\pi })$ for part a

then for part b, I have

$<x>=0$

$<x^{2}>=a^{3}$

$\sigma =a^{2}$

Answer 1

A) 2. 2- 2 2- 2 ITA 2a

ta 2 +00

12 42 2. 21 a 12 乙 -10

-A kla KIT e IT e k A Фор) = alt 2A卞

ナハ 20 卞 2aPI 2AP 2a 2a -00

0 2a2 2a 2C