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Understanding Wavepackets in Particle Physics

Explore the concepts of plane wave eigenstates, free particle propagation, scattering states, and wavepacket reflections. Learn how to calculate momentum expectation values and analyze moving wavepackets. Discover the behavior of wavepackets with boundary conditions and reflection from hard walls. Access instructive animations for visual explanations.

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Understanding Wavepackets in Particle Physics

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  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

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