IB DP Physics: HL复习笔记12.1.10 Tunnelling


  • 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 emitted12-1-10-tunneling-3-ib-hl

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