Prüfer transformation and its application to the numerical description of the motion of quantum particles with various spins in the fields of classical black holes

V. P. Neznamov^a^,*^,**, I. I. Safronov^a^,***, and V. E. Shemarulin^a^,****

^aThe Russian Federal Nuclear Center, All-Russian Scientific Research Institute of Experimental Physics, Sarov, Russia

email: *vpneznamov@vniief.ru
email: **vpneznamov@mail.ru
email: ***IISafronov@vniief.ru
email: ****VEShemarulin@vniief.ru

Received 15 April, 2022

Abstract— Stable and reliable numerical integration of second-order radial equations in the fields of classical black holes can be performed by using the Prüfer transformation and by passing to the use of phase functions, which allows uniquely selecting the solutions with physical asymptotics in numerical calculations.

Keywords: stationary states, black holes, second-order equations, Prüfer transformation and phase functions, singular points and their classification

DOI: 10.1134/S0040577923010051