Summary of One-Dimensional Systems

1. Zero Potential

Physical Example: Proton in beam from cyclotron

Significant Feature: Results used for other systems

2. Step Potential (energy below top)

Physical Example: Conduction electron near surface of metal

Significant Feature: Penetration of excluded region

3. Step Potential (energy above top)

Physical Example: Neutron trying to escape nucleus

Significant Feature: Partial reflection at potential discontinuity

4. Barrier Potential (energy below top)

Physical Example: $\alpha$-particle trying to escape Coulomb barrier

Significant Feature: Tunneling

5. Barrier Potential (energy above top)

Physical Example: Electron scattering from negatively ionized atom

Significant Feature: No reflection at certain energies

6. Finite Square Well Potential

Physical Example: Neutron bound in nucleus

Significant Feature: Energy quantization

7. Infinite Square Well Potential

Physical Example: Molecule strictly confined to box

Significant Feature: Approximation to finite square well

8. Simple Harmonic Oscillator Potential

Physical Example: Atom of vibrating diatomic molecule

Significant Feature: Zero-point energy

9. Periodic Potential

Physical Example: Electron in lattice

Significant Feature: Energy band and energy gap

Problem