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Wavepackets etc.

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

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Wavepackets etc.

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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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