Uncertainty in position for eigenstates (Liboff 3.10)

[WyoChuck]

[STRIKE][/STRIKE]

Homework Statement

From Liboff edition 4:

For the state

ψ(x,t)=A exp(x-x₀)² / {4a²} * exp(ip₀x)/hbar * exp (-iω₀t)

show that (Δx)² = a²

then argue the consistency of this conclusion with the change in shape that |ψ²| suffers with a change in the parameter a

Homework Equations

Equations given in problem as well as

(Δx)² = <(x-<x>²)>

The Attempt at a Solution

So far I've tried substituting in Δx and using algebra to eliminate variables as well as solving for just a but unfortunately have been unable to make and leeway into proving the solution. In general I'm just lost as to where to start and any usefull advice will come in quite handy.

 

[vela]

[STRIKE][/STRIKE]

Homework Statement

From Liboff edition 4:

For the state

ψ(x,t)=A exp(x-x₀)² / {4a²} * exp(ip₀x)/hbar * exp (-iω₀t)

show that (Δx)² = a²

then argue the consistency of this conclusion with the change in shape that |ψ²| suffers with a change in the parameter a

Homework Equations

Equations given in problem as well as

(Δx)² = <(x-<x>²)>

The Attempt at a Solution

So far I've tried substituting in Δx and using algebra to eliminate variables as well as solving for just a but unfortunately have been unable to make and leeway into proving the solution. In general I'm just lost as to where to start and any usefull advice will come in quite handy.

I have no idea what "substituting in Δx and using algebra to eliminate variables as well" means. Show your actual work.