• Single potential wells?lead to quantised energy levels and their associated?wavefunctions
  • The wavefunction extends throughout space

• However, for?infinitely deep square wells?the wavefunctions are localised within the well region
  • The probability of finding the quantum particle at the barrier is zero

• For a?finite barrier, the wavefunction can penetrate the barrier
  • So, the particle has some probability of being in a “classically forbidden region”
• If there are two well-like regions, the solution of Schrodinger’s equation gives an energy level and wavefunction that extends over the whole region of the potential well
• When the red wave function is squared it gives the probability of finding the particle in a particular region of space
• Since the wave function extends through the barrier this means there is a finite probability of finding the particle in?either?of the two well regions

A thin barrier or classically forbidden region can result in tunnelling

• Consequently, if a quantum particle were placed in the narrow well on the right, it is possible at some time later to find it in the region on the left
  • The particle is said to have?tunnelled?through the?narrow barrier

Tunnelling & Alpha Decay

• The?strong nuclear force?within the nucleus is represented by the?square well

• Nucleons in the nucleus have?quantised energy levels?and?wave functions
  • An alpha particle can gain energy and occupy an excited energy level where the?barrier width?is?smaller

• As a result, the alpha particle can tunnel through the classically forbidden region
  • This greatly?increases?the?probability of the alpha particle being emitted

Alpha decay through quantum mechanical tunnelling

Uses of Quantum Tunnelling

• Quantum tunnelling is utilised in several systems, for example in:
  • Semiconductor devices
  • Fusion reactions in the Sun
  • A scanning tunnelling microscope

• In one mode of operation of a scanning tunnelling microscope, a sharp point, one atom thick, is maintained close to a surface
  • This is so that a small tunnelling?current?between the tip and the surface remains?constant
  • In this case, the gap between the tip and the sample surface acts as the barrier that the?electrons?must tunnel through

• The tip is moved up and down and across the surface by?piezoelectric transducers?allowing the sample surface to be mapped out

Simplified schematic of a scanning tunnelling microscope