Well, sigma x comes out to 1/rad(2) for the sqrt((integral from -inf to +inf of Psi* x^2 Psi) - (integral from -inf to +inf of Psi* x Psi)^2).
How would I change the wave function to make sigma x = 1 then?
Yeah, that's how I've been getting <x>.
It must the be exp^(i x) that's causing the problems. The x in the exponent must be messing something up.
How can I get around this?
I have tried this, the only problem is that the function must also have the momentum, -h bar, which requires another exponential term, exp(-i x).
Also, sigma^2 would be 1, and that would have the form A * exp^(-i x)*exp^((-(x+1)^2)/2) where A = 1/ pi^(1/4)
Because of the first exponential...
For some reason, I just can't find the function.
I don't know how I could make a wave function that could possibly have a standard distribution of 1 and an expected value of -1, graphically.
Homework Statement
Come up with a wave function Psi[x] that satisfies the given known values:
<x>=-1
sigma x = 1
<p> = h bar
Homework Equations
The Attempt at a Solution
So far I have this equation, which satisfies <x>, <p>, but not sigma x.
1/[Pi]^(1/4) E^(i (x + 2)) E^(-(1/2)...