# Calculate the probability that the electron is in the range

1. Oct 19, 2004

### harpua

Was just wondering if anyone could help me w/ this question.

Consider the wave function
(psi (x,t)) = (1/sqrt(2))[u2(x)exp(-iE2t/h(bar) + u3(x)exp(-iE3t/h(bar)}. calculate the probability that the electron is in the range (0,L/2) as as function of time. What is the period of oscillation of the probability? NOTE: the wavefuctions u2(x) and u3(x) refer to the n=2 and n=3 states of the infinite well located at 0<x<L.

any help would be appreciated.

2. Oct 19, 2004

### Kane O'Donnell

I'm guessing that $$u_3(x)$$ is supposed to have a coefficient of $$\frac{1}{\sqrt{2}}$$ (so that the wavefunction is normalised).

What you have to do is do calculate the probability integral for 0 < L < L/2. That is, do the integral from 0 < x < L/2 of $$\Psi^{*}\Psi$$. You'll notice that the probability density $$\Psi^{*}\Psi$$ is no longer time-independent! It will wobble between being the u2 probability density and being the u3 probability density - figuring out the period of oscillation shouldn't be too hard once you have the density function sorted out.

Cheerio!

Kane

Last edited: Oct 19, 2004