1. 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”)

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

3. 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.