1. Quantum Tunneling

2. Seeing the world in a new way…

10. Tunneling and the Strange Tales of Exponential Tails!
In an “allowed” region a wavefunction can be wave-like
In a forbidden region a wave function must exponentially tend to zero
Wave function must “look like” this mathematically:

11. How tunneling works…
The amplitude of the wavefunction drops rapidly (exponentially) in the forbidden region – BUT!
If there is still enough amplitude when the quanton reaches the “other side” it can enter a new allowed region

12. The Scanning Tunneling Electron Microscope (STEM)
A current can tunnel across the gap between the subject and the small tip at the end of the crystal controlled probe – this is VERY sensitive to distance
STEMs are capable of spatial resolution on the order of nm or about 1/100th the diameter of an atom!!

13. The Math behind tunneling…
Let V be the potential in the forbidden region (E < V)
Solve
Re-arrange
Use the following for Psi – find b

14. By comparing the size of the wavefunction on either side of the forbidden region we can calculate how many quantons (ie – the current) that tunnels. This depends very delicately on the width of the forbidden region