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Unbound States

Unbound States. A review on calculations for the potential step. Quiz 10.23 Topics in Unbound States: The potential step. Two steps: The potential barrier and tunneling. Real-life examples: Alpha decay and other applications. A summary: Particle-wave propagation. today.

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Unbound States

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  1. Unbound States A review on calculations for the potential step. Quiz 10.23 Topics in Unbound States: The potential step. Two steps: The potential barrier and tunneling. Real-life examples: Alpha decay and other applications. A summary: Particle-wave propagation. today

  2. The Schrödinger Equation: When When When Solution: The potential step: solve the equation Initial condition: free particles moving from left to right. Trans. Inc. Refl. Apply normalization and wave function smoothness

  3. The Schrödinger Equation: When When When Solution: Inc. Refl. The potential step: solve the equation Initial condition: free particles moving from left to right.

  4. When Reflection probability: When Penetration depth: The potential step: transmission and reflection Reflection probability: Transmission probability: Transmission probability:

  5. When When Two steps: The potential barrier and tunneling. Initial condition: free particles moving from left to right.  Tunneling Solution: Solution: Inc. Refl. Inc. Refl. Trans. Trans. Apply normalization and wave function smoothness

  6. When When Two steps: The potential barrier and tunneling.  Tunneling Results: Results: Resonant transmission. Thin film optics analogy.

  7. Tunneling through a wide barrier Wide barrier: Tunneling: Transmission probability is very sensitive to barrier width L and the energy E. This leads to some wonderful applications of QM.

  8. Real-life examples: Alpha decay and other applications. Who took my cheese? Who took the energy from my alphas?

  9. Scanning Tunneling Microscope Please read about the tunneling diode, field emission and the SQUIDS yourself. We will discuss about the STM here.

  10. A summary: Particle-wave propagation.

  11. Review questions • Please review the solutions to the Schrödinger equation with the step and two steps condition and make sure that you feel comfortable with the results.

  12. Preview for the next class (10/28) • Text to be read: • Please skim from 7.1 to 7.8. If you have difficulty in understanding the materials, see the slides by next Monday. • Questions: • What is the fundamental change to move the Schrödinger equation from 1-D to 3-D? • What is the quantization condition for the z component of angular momentum? • According to QM, can you have a visual presentation for the electron’s whereabouts in a hydrogen atom?

  13. Homework 9, due by 10/30 • Problem 21 on page 224. • Problem 24 on page 225. • Problem 32 on page 225.

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