# Electron in a potential well of specified thickness

1. Jan 15, 2012

### solas99

an electron in a potential well of thickness (e.g 1nm) with infinitly high potential barriers. it is in the lowest possible energy state.

to calculate the energy of the electron. i used:

E=(n^2 pi^2 h(bar)^2)/ (2m Lz^2)

which will result in approx 10E-19 j

my question is, how can tackle a situation, when asked to find the probability of finding the electron between 0.1nm and 0.2nm from one side of well?

do i try to use the same equation but change the value of Lz to (0.2-0.1)=0.1nm?

2. Jan 15, 2012

### jonmohajer1

Do you know the wavefunction that governs a particle in this situation? (1 dimensional box conditions, infinite potential well)?
Think about how this wave function is normalised in accordance with the boundary conditions- we say the probability of finding the electron somewhere in the range 0 to L (L=1nm) must be equal to 1. With this normalised wave function you can then ask for the probability of finding the electron in range 0.1nm to 0.2nm. i.e. the limits of your integral for the probability become 0.1nm to 0.2nm.