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

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Presentation transcript:

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

Wavepackets withNormalization: Linear superpositions of plane wave solutions

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

Propagator is a free particle propagator “imaginary time”

Calculate evolution of the wavefunction using the propagator

Example 2: Gaussian wavepacket

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

Example 4: wavepacket reflected from a hard wall Boundary condition: Eigenstates: Propagator: 0 x0

Wavepackets reflected from steps & barriers For very nice and instructive animations visit

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