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Barrier Penetration and Quantum Mechanical Tunneling

Barrier Penetration and Quantum Mechanical Tunneling. The potential "barrier" defined. …but what if we “turn it upside down”? This is a finite potential barrier. We’ve learned about this situation: the finite potential well…. I. II. III. U. E. -L/2. L/2.

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Barrier Penetration and Quantum Mechanical Tunneling

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  1. Barrier Penetration and Quantum Mechanical Tunneling

  2. The potential "barrier" defined …but what if we “turn it upside down”? This is a finite potential barrier. We’ve learned about this situation: the finite potential well… I II III U E -L/2 L/2 When we solved this problem, our solutions looked like this… What would you expect based on your knowledge of the finite box?

  3. A classical analogy: more evidence of wavelike behavior Total Internal Reflection (in actuality the light field in the optically dense space is evanescent, i.e. exponentially decaying) Frustrated Total Internal Reflection

  4. Frustrated Total Internal Reflection: dependence on layer thickness Below, the thick curves show the reflectance as the thickness of the low-index layer (air) changes from 10 to 900 nm. Note that as the layer thickness increases, the reflectance becomes closer to total at 41 degrees. That is, FTR gives way to TIR.

  5. wave packet approaching a barrier Qualitatively:

  6. Pedagogical exercise: consider time independent case (pure momentum states) to the left of the barrier to the right of the barrier Instructive to consider the probability of transmission and reflection… R+T=1 of course…

  7. E>U case

  8. Field emission microscope

  9. Real world example: field emission + + + + + + + + + + + e 0 x U(x)=-eex E -U 0

  10. Application: alpha decay

  11. Why does the half life vary more than the kinetic energy?

  12. U(r) kinetic energy of escaping alpha particle E r R alpha decay

  13. Real world application: smoke detector

  14. An aside: another kind of smoke detector The photoelectric detector Without smoke With smoke

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