# Commutative free particle time evolution

1. Nov 26, 2012

### chaotic

1. The problem statement, all variables and given/known data

http://img853.imageshack.us/img853/2532/70224197.png [Broken]

2. Relevant equations

i know schrödingher eq. and basic quantum formula

3. 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?

Last edited by a moderator: May 6, 2017
2. Nov 27, 2012

### chaotic

i even dont know what is the time evoluation of varience? what is that?

3. Nov 27, 2012

### vela

Staff Emeritus
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).

4. Nov 27, 2012

### chaotic

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

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

ψ = ∫ $\frac{iħ}{2m}$ d2ψ/dx2 dt

but i dont know how can i take the integral of right side?

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

is that true?

5. Nov 27, 2012

### vela

Staff Emeritus
I have no idea what you're doing.

6. Nov 27, 2012

### chaotic

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