### Question

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