Editing Electron Tunneling (section)

== Why This Works ==

As is demonstrated at the beginning of this demo, a large object cannot tunnel through a thick barrier unless it has a high amount of energy. However, this changes when we look at atoms and electrons, where an electron can sometimes make it through a barrier when it lacks the energy to do so. ''Electron Tunneling'' is the phenomenon which allows electrons to travel through barriers that they otherwise shouldn’t be able to go through. To understand what really happens with electron tunneling, one needs to look at the time-independent Schrödinger equation for particle-wave duality:
{| class="wikitable" style="color:black; background-color:#ddd; margin-right: 20; text-align: left"
|+ Time Independent Schrödinger Equation
|''d''<sup>2</sup> / ''d''x<sup>2</sup>  '''Ψ'''(x) = (2m) / ('''ħ'''<sup>2</sup>)  '''M'''(x)  '''Ψ'''(x)
| '''M'''(x): Quantified Energy of the Particle
| '''M'''(x)= ('''V'''(x) - '''E'''(x))
|-
|If '''M'''(x) is constant and positive:
| '''V'''(x): Potential Energy
| '''E'''(x): Kinetic energy (x-axis)
|-
|(2m)/('''ħ'''<sup>2</sup>) '''M'''(x) '''Ψ'''(x) = '''κ'''<sup>2</sup> '''Ψ'''(x)
|Where '''κ'''<sup>2</sup> = (2m)/('''ħ'''<sup>2</sup>) '''M'''
| '''ħ''': "h-bar", or the Planck Constant (h)/2pi
|-
|If '''M'''(x) is constant and negative:
| 
| '''Ψ'''(x): The Wave Function
|-
|(2m)/('''ħ'''<sup>2</sup>) '''M'''(x) '''Ψ'''(x) = - '''k'''<sup>2</sup> '''Ψ'''(x)
|Where '''k'''<sup>2</sup> = - (2m)/('''ħ'''<sup>2</sup>) '''M'''
| m: Mass of the Particle
|}
Without going too deeply into the math, we can make out what the equations are saying. The first equation is showing the second derivative of the time independent Schrödinger equation. This means that we are looking at the Schrödinger equation without the time factor, and the only factors we will focus on are: 
* The mass of the particle, m
* The quantified energy of the particle, '''M'''(x)

We know what the mass of an electron is, so we need to solve for the energy of our particle. If the particle has a positive and constant '''M''' value, then we can solve for '''κ'''<sup>2</sup>. If the value is negative, then we are solving for '''k'''. In either case, we will be solving for the ''Probability'' of the particle making it through the barrier.

If a particle has really high energy, it might be able to make it over the barrier without having to tunnel through. This we represent with the ball being thrown over the barrier. Although this is good for our particle, it is not the effect we are looking for with the particle. Instead, we are looking for any situations where the particle ''doesn't'' have the energy to go over the barrier, but manages to somehow make it to the other side. This is because the particle, although it doesn’t go ''over'' the barrier, still has some chance of going ''through''. 

The probability of a particle making it through a barrier can be thought of as a percentage comparison. If the potential energy of a particle is equal to, for example, 70% of the energy barrier’s value, then the particle would have a 70% chance of tunneling through the barrier on the first try. This is because tiny particles can also behave like waves, in what is called ''Particle-Wave Duality''. This means a particle can travel through a barrier by acting like a wave instead of a particle. This allows electrons to get through energy barriers that they should be blocked by, since their wave function can potentially last long enough to make it through rather than the physical particle bouncing off! This is what is demonstrated at the end with the sleight of hand trick; The particle somehow makes it through the barrier without bouncing off, even though it didn't have the energy to go over the barrier.