Quantum Tunneling

Seeing the world in a new way…

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:

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

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 0.001 nm or about 1/100th the diameter of an atom!!

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

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