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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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Plane wave eigenstates: Free particle x Wavepackets etc. • scattering states • non-normalizable • continuous spectra
Linear superpositions of plane wave solutions with Normalization: Wavepackets
Example 1 Unfortunately, the integrand is badly behaved and difficult to evaluate even numerically.
is a free particle propagator “imaginary time” Propagator
Calculate evolution of the wavefunction using the propagator
Calculate the momentum expectation value: Example 3: moving Gaussian wavepacket How do we know this is a moving wavepacket?
Boundary condition: Eigenstates: 0 0 x Propagator: Example 4: wavepacket reflected from a hard wall
For very nice and instructive animations visit http://www.quantum-physics.polytechnique.fr/en/pages/p0103.html Wavepackets reflected from steps & barriers