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Understanding Quantum Wavepackets: Propagation and Reflection Examples

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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.

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Understanding Quantum Wavepackets: Propagation and Reflection Examples

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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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