Partial%20wave%20expansion%20of%20the%20plane%20wave

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Partial wave expansion of the plane wave
Sum over spherical waves
Angular dependence of the spherical wave
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One partial wave (standing wave made of incoming
and outgoing waves)
Plane wave (incoming wave)
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Sum of two partial waves
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Sum of three partial waves
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Sum of five partial waves
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Sum of ten partial waves
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Sum of twenty partial waves
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Sum of thirty partial waves
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Gaussian repulsive potential w(r) exp(0.04 r2)
The potential (red line is the energy)
Phase shift vs. angular momentum for partial waves
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Plot of trajectories on the potential surface
Mapping (y, t) gt (qx, qy)
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Exact
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Semiclassical
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Absolute value. Left - exact, right -
semiclassical