What are the odds of me experiencing Quantum Tunneling?

Asked by: Matt

Answer

The short answer is very very low. For the long, ugly answer, read on.

The probability of an object tunneling through a barrier as predicted by the Schrodinger equation can be found by the equation

P= e^(-2KL)

Where L is the width of the barrier and K is the wave number, which is equal to [sqrt(2m(V-E))]/h

Where m is the mass of the object that we want to tunnel, V is the potential energy of the barrier, E is the energy of the tunneling object (usually kinetic), and h is Plank's Constant divided by 2*pi (approximately 1.06x10^-34 J*s)

So let's take a look at all the above, since the exponent of the probability function is proportional to mass and barrier length, we can see that the probability of tunneling decreases exponentially as you increase mass and barrier length.

So, if you were 50kg, and were attempting to tunnel through a 30 joule potential barrier (equivalent to you trying to toss a 1kg object 3 meters in the air) which was 1 m wide, while running at 1m/s, the probability of you tunneling through would be approximately equal to:

P= e^{(-2((sqrt(100(30-25)))/h)(1))} = e^{(-4.219x10^35)}

... which is so small it is almost zero. So once again, for a human being the answer is: almost impossible. However for objects with extremely small masses (such as electrons) the probability can be quite high.
Answered by: Loren Chang, Physics Undergrad, UC Irvine