Commutative free particle time evolution

[chaotic]

Homework Statement

http://img853.imageshack.us/img853/2532/70224197.png

Homework Equations

i know schrödingher eq. and basic quantum formula

The Attempt at a Solution

i showed that the equality at the first question but i can not start from (a) part. how and where am i supposed to start for (a) part of question?

 

[chaotic]

i even don't know what is the time evoluation of varience? what is that?

 

[vela]

Forget quantum mechanics for a second. From basic statistics, if x is a random variable, its variance is $\sigma^2 = E[(x-\bar{x})^2]$, where $\bar{x}=E(x)$. Now how does this translate into quantum mechanics? It should be clear how the first part of the problem then applies to solving (a).

 

[chaotic]

thank you for your answer. now i am trying that

$\frac{dψ}{dt}$ = $\frac{iħ}{2m}$ d²ψ/dx²

after that i find that; (i send dt to right side)

ψ = ∫ $\frac{iħ}{2m}$ d²ψ/dx² dt

but i don't know how can i take the integral of right side?

after that i will use the <x> = ∫ψ^* x ψ

is that true?

 

[vela]

I have no idea what you're doing.

 

[chaotic]

me too. I am very confused. can you just tell me how can i find <x(t)> and <x(t)^2>