Unbound States 1. A review on calculations for the potential step. 2. Quiz 10.23 3. Topics in Unbound States:  The potential step.  Two steps: The potential.

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Presentation transcript:

Unbound States 1. A review on calculations for the potential step. 2. Quiz 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

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

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

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

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

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

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.

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

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

A summary: Particle-wave propagation.

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. 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.

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

Homework 9, due by 10/30 1. Problem 21 on page Problem 24 on page Problem 32 on page 225.