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