Theory of Quantum Mechanical Scattering in Hyperbolic Space
L. L. Jenkovszky,
Y. A. Kurochkin,
V. S. Otchik,
P. F. Pista,
N. D. Shaikovskaya,
D. V. Shoukavy
Affiliations
L. L. Jenkovszky
Bogolyubov Institute for Theoretical Physics, National Academy of Sciences of Ukraine, Metrolohichna Str. 14b, 03143 Kiev, Ukraine
Y. A. Kurochkin
B.I. Stepanov Institute of Physics, National Academy of Sciences of Belarus, 68-2 Niezaliežnasci av., 220072 Minsk, Belarus
V. S. Otchik
Department of Natural Sciences, Civil Protection University, Ministry for Emergency Services of Belarus, Mashinostroitelei Str. 25, 220118 Minsk, Belarus
P. F. Pista
Ukrainian-Hungarian Education Institute, Uzhgorod National University, University Str. 14/A, 88000 Uzhgorod, Ukraine
N. D. Shaikovskaya
B.I. Stepanov Institute of Physics, National Academy of Sciences of Belarus, 68-2 Niezaliežnasci av., 220072 Minsk, Belarus
D. V. Shoukavy
B.I. Stepanov Institute of Physics, National Academy of Sciences of Belarus, 68-2 Niezaliežnasci av., 220072 Minsk, Belarus
The theory of quantum mechanical scattering in hyperbolic space is developed. General formulas based on usage of asymptotic form of the solution of the Shrödinger equation in hyperbolic space are derived. The concept of scattering length in hyperbolic space, a convenient measurable in describing low-energy nuclear interactions is introduced. It is shown that, in the limit of the flat space, i.e., when ρ→∞, the obtained expressions for quantum mechanical scattering in hyperbolic space transform to corresponding formulas in three-dimensional Euclidean space.
