In-class group activity 9:

Exploring bound states in potential wells

Use an on-line simulation from the University of Colorado PhET group to explore the properties of quantum "particles" bound in potential wells.  
Link to the simulation http://phet.colorado.edu/en/simulation/bound-states.  Click "Run Now!"

• Explore the interface. There are some non-obvious controls.

  • You can select which wave function is shown in the bottom graph by moving your mouse over the corresponding energy level and clicking.  The bottom graph will also show a highlight of the state that your mouse is over, so you can compare two states.

  • You can change the configuration of the potential energy by dragging the lines on the graph, clicking or Configure Potential, or using the Potential menu.

  • You can use the Colors menu to change the color scheme.

• Start with an electron (particle mass m_e) in the default square well (width 1 nm, height 10 eV).

  • Examine the stationary state wave functions ψ(x,t) = ψ(x) exp(-iEt/ħ) and the probability densities  |ψ(x,t)|² = |ψ(x)|² for different  energy eigenvalues.

  • Vary the height of the potential depth   Describe the changes in ψ(x,t) and  |ψ(x,t)|².  Explain why the wave functions changes in the way shown in the simulation.

  • Vary the width of the potential depth   Describe the changes in ψ(x,t) and  |ψ(x,t)|².  Explain why the wave functions changes in the way shown in the simulation.

  • How do  the energies change with particle mass?

• Now switch to the default asymmetric potential.

  • Examine the stationary state wave functions ψ(x,t) = ψ(x) exp(-iEt/ħ) and the probability densities  |ψ(x,t)|² = |ψ(x)|² for different  energy eigenvalues.

  • Compare these observations with those you made for default square well.  Describe similarities and differences.

• Now switch to the default harmonic oscillator potential.

  • Examine the stationary state wave functions ψ(x,t) = ψ(x) exp(-iEt/ħ) and the probability densities  |ψ(x,t)|² = |ψ(x)|² for different  energy eigenvalues.

  • Compare these observations with those you made for default square well.  Describe similarities and differences.

  Open the Quantum Tunneling simulation https://phet.colorado.edu/en/simulation/legacy/quantum-tunneling

Explore this and note your observations

Also explore the quantum wave interference simulation https://phet.colorado.edu/en/simulation/legacy/quantum-wave-interference

and note your observations