Eikonal approximation for fast-decreasing potentials. I
The Schrödinger equation with a potential gq(x), decreasing faster at infinity than any power of ¦x¦−1, is considered at energy k2. The complete asymptotic expansion of its wave function is constructed for k → ∞ and g≤C2−γ, γ > 0. This expansion is used to derive the asymptotics of the forward scattering amplitude and of the total scattering cross section.
KeywordsWave Function Asymptotic Expansion Scattering Cross Section Forward Scatter Scattering Cross
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