# Numerical calculation of tunneling probability

1. Dec 3, 2007

### chandanrupa

Hi, I am trying to numerically calculate the tunneling probability for a wave function |psi> as a function of x. I have a double well potential. The wave function is initially in the left well. I do not know what exactly I have to find to show tunneling: the probability of being on the left well or the average value of x to see how it varies with time or something else. I need someone's help about this.

2. Dec 3, 2007

### Mephisto

it is my understanding that tunneling is basically if a particle gets to a classically forbidden region... i.e. jumping over a potential barrier that it doesnt have enough energy to get through. The probability of tunneling would then be the integral of the wave function squared over the region that it should not be in. So to find the tunneling probability to get to the right part of the well, you are trying to find the probability that the particle is on the right, somewhere. (that's of course given that it doesnt have enough energy to get there without tunneling)
that's my understanding, but I only took 2 courses in Quantum Mechanics, so I'm still very much a newbie :)