2born (2born) wrote,

Новый интеграл с бесселями взят!

Ответ, правда, немножко громоздкий, но то мелочи:))))

The Integral Over 2 Spherical Bessel Functions Multiplied by a Gaussian: https://arxiv.org/abs/1908.07374

In this paper, the integral (λ10λ20λ30)∫∞0rλ3+2exp(−αr2)jλ1(k1r)jλ2(k2r)dr, where k1, k2 and α are positive, is evaluated analytically. The result is a finite sum over the modified spherical Bessel function of the first kind. This result will be useful for nuclear scattering calculations, where harmonic oscillator nuclear wavefunctions are used or when evaluating momentum space matrix elements for a Gaussian potential.

7 pages
Tags: Мегаучебник или Что я читал и похвалил, наука, разгребая arXiv'ы

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