Numerical calculation of tunneling probability

[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.

 

[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 doesn't 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 doesn't 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 :)

 

[denian]

Hi there,

Calculating the tunneling probability for a wave function |psi> as a function of x can be a complex task. The tunneling probability is a measure of the likelihood that a particle will pass through a potential barrier, such as the double well potential you described. It is important to note that this probability is not a constant value, but rather a function of both the energy of the particle and the shape of the potential barrier.

To calculate the tunneling probability, you will need to use a numerical method, such as a Monte Carlo simulation, to solve the Schrödinger equation for your wave function |psi>. This will allow you to determine the probability of the particle being in the left well or tunneling to the right well at a given point in time.

Alternatively, you could also calculate the average value of x for the wave function |psi> over time to see how it varies. This would give you an indication of the particle's position and how it evolves over time.

I would recommend consulting with a physicist or using a specialized software program to assist with your calculations. Additionally, further research on the topic of tunneling probability and its calculation may also be helpful.

I hope this helps and good luck with your calculations!