Corpus ID: 201103759

The Integral Over 2 Spherical Bessel Functions Multiplied by a Gaussian.

@article{Mehrem2019TheIO,
  title={The Integral Over 2 Spherical Bessel Functions Multiplied by a Gaussian.},
  author={R. Mehrem},
  journal={arXiv: Nuclear Theory},
  year={2019}
}
  • R. Mehrem
  • Published 2019
  • Physics
  • arXiv: Nuclear Theory
In this paper, the integral $\pmatrix{\lambda_1 &\lambda_2 &\lambda_3\cr 0 &0 &0\cr}\, \int_0^\infty \, r^{\lambda_3+2}\, \exp{(-\alpha r^2)}\, j_{\lambda_1}(k_1r) \,j_{\lambda_2}(k_2r) \,dr$, where $k_1$, $k_2$ and $\alpha$ 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… Expand

References

SHOWING 1-8 OF 8 REFERENCES
APPL
Statistical packages have been used for decades to analyze large datasets or to perform mathematically intractable statistical methods. These packages are not capable of working with random variablesExpand
Satchler, Angular Momentum (Oxford
  • 1962
Angular Momentum in Quantum Mechanics
This book offers a concise introduction to the angular momentum, one of the most fundamental quantities in all of quantum mechanics. Beginning with the quantization of angular momentum, spin angularExpand
Table of Integrals, Series, and Products
Introduction. Elementary Functions. Indefinite Integrals of Elementary Functions. Definite Integrals of Elementary Functions. Indefinite Integrals of Special Functions. Definite Integrals of SpecialExpand
"J."
however (for it was the literal soul of the life of the Redeemer, John xv. io), is the peculiar token of fellowship with the Redeemer. That love to God (what is meant here is not God’s love to men)Expand