# Probability Density in Quantum Mechanics

1. Oct 26, 2008

### youngoldman

I am trying to calculate the variance of the position of a particle in a one dimensional box (quantum mechanics).

I have a wavefunction, and I know the probablilty density is the integral of (the wavefunction squared) with respect to x.

Can you please tell me how this wavefunction could be plugged in to the variance formula

var(x) = αŦ(x - µ)²α

(the expected value = a/2 where a is the distance between the walls)

2. Oct 26, 2008

### jhicks

$$var(x) = <x^2> - <x>^2 = \int_{-\infty}^{\infty}\Psi^{*}(x) x^2 \Psi(x)dx - a^2/4$$, since <x> = a/2 and $$\Psi(x)$$ is the wavefunction.