1 / 10

Understanding Quantum Wavepackets: Propagation and Reflection Examples

Explore free particle eigenstates, scattering states, and wavepacket normalization. Calculate wavefunction evolution and momentum expectation values for various scenarios. Visualize wavepacket reflections and animations for deeper understanding.

caldwell-dunlap
Télécharger la présentation

Understanding Quantum Wavepackets: Propagation and Reflection Examples

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Plane wave eigenstates: Free particle x Wavepackets etc. • scattering states • non-normalizable • continuous spectra

  2. Linear superpositions of plane wave solutions with Normalization: Wavepackets

  3. Example 1 Unfortunately, the integrand is badly behaved and difficult to evaluate even numerically.

  4. is a free particle propagator “imaginary time” Propagator

  5. Calculate evolution of the wavefunction using the propagator

  6. Example 2: Gaussian wavepacket

  7. Calculate the momentum expectation value: Example 3: moving Gaussian wavepacket How do we know this is a moving wavepacket?

  8. Boundary condition: Eigenstates: 0 0 x Propagator: Example 4: wavepacket reflected from a hard wall

  9. For very nice and instructive animations visit http://www.quantum-physics.polytechnique.fr/en/pages/p0103.html Wavepackets reflected from steps & barriers

More Related