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note
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ψ(s) defines a curve on the complex ψ-plane. The curve is the well-known Cornu spiral [18], the two centers of which are at ψ = exp[±iπΦ̃]; For y varying from -∞ to ∞, ψ(x,y) changes along the spiral from ψ = exp[-iπΦ̃] to ψ = exp[iπΦ̃].
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27
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0040189090
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note
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Some caution is needed because of the discontinuity of ψ(+0, y) in eq. (4) at y = 0. The correct limiting procedure, where details of the behaviour at y = 0 are unimportant, is the following; ∂ψ/∂y is substituted by (ψ(+0, y + a) - ψ(+0, y -a))/2a and the limit a → 0 is taken after the y-integration.
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0040783602
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