- #1
QFT25
- 25
- 3
Homework Statement
Consider a particle of mass m subject to a one-dimensional potential of the following form:
(1/2)k*x^2 x>0
Infinity for 0<x
Find <x^2> for the ground state
Homework Equations
<x^2>= <Psi|x^2|Psi>
The Attempt at a Solution
I know the answer is 3*h/(4*m*w) but to me that makes no sense. That answer was derived using the first excited state of the ground state for the potential in which there is no infinite wall at x=0. That state is normalized for -Infinity to Infinity. But in our circumstance the motion can only be from 0 to Infinity. That means I need to re-normalize the wave function so that it it's norm is 1 from 0 to Infinity. When I do that and calculate the expectation value I get 3*h/(2*m*w). I don't understand how you can use a wave function which is not normalized from 0 to Infinity to calculate < x^2> from 0 to infinity