An Experimentalists View on the Analogy between Step Edges and Quantum Mechanical Particles

Guided by scanning tunnelling microscopy images of regularly stepped surfaces it will be illustrated that there is a striking similarity between the behaviour of monoatomic step edges and quantum mechanical particles (spinless fermions). The direction along the step edge is equivalent to the time, while the direction perpendicular to the step corresponds to the one-dimensional space along which the quantum mechanical particles are located. The non-crossing condition of the steps, giving rise to entropic repulsion, is related to the boundary condition of the wavefunction of a quantum mechanical particle at an infinitely high barrier. Finally, the step edge stiffness can be related to the mass of the quantum mechanical particle.