Last hour: Particles at step functions

•Ansatz (approach) dependent on region and energy of the particle:

classically allowed

oscillating solution,

classically forbidden

exp. decaying solution,

•WF and its first derivative must be matched at discontinuity

•Single step from V(x)=0 to V(x)=V0:

E > V0 results in partial reflection

E ≤ V0 results in complete reflection, but WF penetrates into classically

forbidden region (“evanescent wave”)

ikxikx eAeAxxVE ')(:)(

20 )(2

VEm

k

xx eBeBxxVE ')(:)(

20 )(2

EVm

< from Cohen-Tannoudji et al. “Quantum Mechanics” >

Resonance Scattering

Learning Goals for Chapter 8 – “Rectangular” Potentials

After this chapter, the related homework problems, and reading the relevant

parts of the textbook, you should be able to:

•use the boundary conditions at a step to derive reflection and transmission coefficients;

•explain the phenomenon of evanescent waves and some examples of their application;

•explain the phenomenon of tunneling and some examples of its application;

•explain the phenomenon of resonance scattering.