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Confluent hypergeometric expansions of the confluent Heun function governed by two-term recurrence relations
T. A. Ishkhanyan, V. P. Krainov, A. M. Ishkhanyan
We show that there exist infinitely many nontrivial choices of parameters of the single confluent Heun equation for which the three-term recurrence relations governing the expansio…
Rational solutions of (1+1)-dimensional Burgers equation and their asymptotic
V. I. Avrutskiy, V. P. Krainov
A special initial condition for (1+1)-dimensional Burgers equation is considered. It allows to obtain new analytical solutions for an arbitrary low viscosity as well as for the inv…
WKB-approach for the 1D hydrogen atom
A. M. Ishkhanyan, V. P. Krainov
Taking into account results of WKB-approximation, we derive exact quantum energies and wave functions of even and odd states in the one-dimensional Coulomb potential
Uncertainty relation for the radial momentum and radial coordinate in the Coulomb potential
A. M. Ishkhanyan, V. P. Krainov
We have obtained the uncertainty relations for arbitrary states of the hydrogen atom. It is shown that the minimal value of the uncertainty relation is attained for the circular Ry…