System of two particles, scattering state, scattering cross section, scattering amplitude, phase shift, quasipotential equation, scattering form-factor, bound state, energy spectrum, decay constant, resonant state.
Subject:
Quantum theory of scattering states and bound states of relativistic two-particle systems.
Quantum theory of resonant states of two-particle systems.
Analytical and numerical methods for solving equations of quantum theory.
Main publications:
V.N. Kapshai, Yu.A. Grishechkin, “Relativistic equations with some point potentials”, Russian Physics Journal, 52:6 (2009), 554-563
Yu.A. Grishechkin, V.N. Kapshai, “Numerical solution of relativistic problems on bound states of systems of two spinless particles”, Russian Physics Journal, 56:4 (2013), 435-443
Yu.A. Grishechkin, V.N. Kapshai, “Solution of the Logunov–Tavkhelidze Equation for the Three-Dimensional Oscillator Potential in the Relativistic Configuration Representation”, Russian Physics Journal, 61:9 (2018), 1645-1652
Yu. A. Grishechkin, A. V. Buzhan, V. N. Kapshai, “Approximate analytical solution of the one-dimensional quasipotential equation with the potential $(\rho^2+\rho_0^2)^{-1}$ in the relativistic configurational representation”, PFMT, 2023, no. 3(56), 12–15
2022
2.
A. V. Paulenko, Yu. A. Grishechkin, “Exact solutions of the two-dimensional Logunov–Tavkhelidze equation with some analogues of the harmonic oscillator potential in the momentum representation”, PFMT, 2022, no. 4(53), 43–45
3.
Yu. A. Grishechkin, V. N. Kapshai, “Approximate analytical solution of the Logunov–Tavkhelidze equation with a linear potential in the relativistic configurational representation”, PFMT, 2022, no. 2(51), 22–25
4.
Yu. A. Grishechkin, V. N. Kapshai, “Approximate analytic solution of the Logunov–Tavkhelidze equation for a one-dimensional oscillator potential in the relativistic configuration representation”, TMF, 211:3 (2022), 455–468; Theoret. and Math. Phys., 211:3 (2022), 826–837
Yu. A. Grishechkin, V. N. Kapshai, “Some solutions of the dispersion equation for a moving biisotropic medium”, PFMT, 2021, no. 2(47), 35–38
2020
6.
Yu. A. Grishechkin, A. V. Paulenko, “Approximate analytical method for solving the schrödinger equation with the Gaussian potential in the momentum representation”, PFMT, 2020, no. 3(44), 18–21
2019
7.
Yu. A. Grishechkin, A. V. Pavlenko, V. N. Kapshai, “On an approximate analytical method for solving the Schrödinger equation with the Gaussian potential”, PFMT, 2019, no. 4(41), 7–10
Yu. A. Grishechkin, V. N. Kapshai, M. S. Danilchenko, “Relativistic bound $s$-states problem for superposition of two potentials «$\delta$-sphere» type”, PFMT, 2017, no. 2(31), 15–19
2015
9.
V. N. Kapshai, Yu. A. Grishechkin, “Relativistic scattering $s$-states problem for superposition of two potentials «$\delta$-sphere» type”, PFMT, 2015, no. 2(23), 7–12
V. N. Kapshai, M. S. Danilchenko, Yu. A. Grishechkin, “Covariant equations and resonance states of two-particle systems with $\delta$-function potentials”, PFMT, 2015, no. 1(22), 11–15
2014
11.
Yu. A. Grishechkin, M. S. Danilchenko, V. N. Kapshai, “Complex scaling method for two-particle equations in the momentum representation and resonance states”, PFMT, 2014, no. 3(20), 21–25
Yu. A. Grishechkin, V. N. Kapshai, “Relativistic scattering problem for two-particle systems with one-boson exchange potentials”, PFMT, 2014, no. 2(19), 13–18
2013
13.
Yu. A. Grishechkin, V. N. Kapshai, “Relativistic bound state problem for two-particle systems with energy dependent one boson exchange potential”, PFMT, 2013, no. 1(14), 24–26
2011
14.
V. N. Kapshai, K. P. Shilyaeva, Yu. A. Grishechkin, “Resonance states of relativistic systems and covariant two-particle equations”, PFMT, 2011, no. 4(9), 33–37
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