View source for Zeldovich regularization

'''Zeldovich regularization''' refers to a [[Physics:Regularization|regularization method]] to calculate [[Improper integral|divergent integrals]] and [[Divergent series|divergent series]], that was first introduced by [[Biography:Yakov Zeldovich|Yakov Zeldovich]] in 1961.<ref>Zel’Dovich, Y. B. (1961). On the theory of unstable states. Sov. Phys. JETP, 12, 542.</ref> Zeldovich was originally interested in calculating the norm of the [[Physics:Gamow factor|Gamow wave function]] which is divergent since there is an outgoing spherical wave. Zeldovich regularization uses a [[Gaussian function|Gaussian]] type-regularization and is defined, for divergent integrals, by<ref>Garrido, E., Fedorov, D. V., Jensen, A. S., & Fynbo, H. O. U. (2006). Anatomy of three-body decay III: Energy distributions. Nuclear Physics A, 766, 74-96.</ref>

:<math> \int_0^\infty f(x)  dx \equiv \lim_{\alpha\to 0^+}\int_0^\infty f(x) e^{-\alpha x^2} dx.</math>

and, for divergent series, by<ref>Mur, V. D., Pozdnyakov, S. G., Popruzhenko, S. V., & Popov, V. S. (2005). Summation of divergent series and Zeldovich’s regularization method. Physics of Atomic Nuclei, 68, 677-685.</ref><ref>Mur, V. D., Pozdnyakov, S. G., Popov, V. S., & Popruzhenko, S. V. E. (2002). On the Zel’dovich regularization method in the theory of quasistationary states. Journal of Experimental and Theoretical Physics Letters, 75, 249-252.</ref><ref>Orlov, Y. V., & Irgaziev, B. F. (2008). On the normalization of the Gamov resonant wave function in the configuration space. Bulletin of the Russian Academy of Sciences: Physics, 72, 1539-1543.</ref>

:<math>\sum_n c_n  \equiv \lim_{\alpha\to 0^+}\sum_n c_n e^{-\alpha n^2}.</math>

==See also==
*[[Abel's theorem]]
*[[Borel summation]]

==References==
{{reflist|30em}}

[[Category:Summability methods]]
[[Category:Concepts in physics]]

{{Sourceattribution|Zeldovich regularization}}