# Quantum tunneling probability density

1. Oct 10, 2007

### swain1

1. The problem statement, all variables and given/known data
When an electron has tunnelled through a potential barrier it's wavefunction is described by a plane wave travelling in the positive x direction. In this region the probability density is constant. I am trying to explain why it is constant but can't find any info in books or on the internet.

2. Relevant equations
f(x)=Fexp(ikx)

3. The attempt at a solution

Have had some ideas which haven't worked out to be right. I now it is something to do with the wavefunction being a plane wave but can't work out why it is constant.

2. Oct 10, 2007

### George Jones

Staff Emeritus
How is probability density expressed in terms of a wavefunction?

3. Oct 10, 2007

### Dick

It's a positive energy solution to the schrodinger equation with no potential. So as you say it's proportional to exp(ikx). To get probability density you take that times it's complex conjugate. What do you get?