I was born in 1957, city Gomel. Graduated from Gomel State University in 1983. Worked (1983-2005) at the Institute of Physics of the National Academy of Sciences of Belarus (Minsk) and Joint Institute for Nuclear Research (Dubna, Russia). Worked at the University of Illinois at Chicago (1995-2005). I am currently working at Gomel State University. My fields of interest are Quantum Mechanics, Bound States, Hadron Physics, High-Energy Particle Physics.
Physical properties of the Cornell potential in the complex-mass scheme are investigated. Two exa... more Physical properties of the Cornell potential in the complex-mass scheme are investigated. Two exact asymptotic solutions of rela tivistic wave equation for the coulombic and linear components of the potential are used to derive the resonance complex-mass for mula. The centered masses and total widths of the leading p-family resonances are calculated.
The hydrogen atom as relativistic two-body problem is considered. Interaction of a proton and an ... more The hydrogen atom as relativistic two-body problem is considered. Interaction of a proton and an electron in the atom is described by the static Lorentz scalar Coulomb potential. Relativistic two-body wave equation is derived. Lagrangian relativistic mechanics is used to derive the two-particle dynamic equation of motion. The proton structure and motion effects are accounted in the calculations. The energy spectrum of the hydrogen atom is calculated and compared with the tabulated NIST data.
Flavored mesons containing quarks of unequal masses are studied. The appropriate tool is the Beth... more Flavored mesons containing quarks of unequal masses are studied. The appropriate tool is the Bethe-Salpeter formalism, but its inherent complexity leads to series of difficulties mostly related to the central role played in it by the relative time or energy. We consider bound states in the spirit of "Constraint Relativistic Quantum Mechanics (RQM)". Interaction of quarks is described by the funnel-type potential with the distant dependent strong coupling, $\alpha_s(r)$. Relativistic bound-state problem is formulated with the use of symmetries, energy-momentum conservation laws in Minkowskiy space. Relativistic two-body wave equation with position dependent particle masses is derived and used to describe the flavored mesons. Free particle hypothesis for the bound state is developed: quark and antiquark move as free particles in of the bound system. Solution of the equation for the system in the form of a~standing wave is given. Interpolating complex-mass formula for two exa...
The hydrogen atom as relativistic bound-state system of a proton and an electron in the complex-m... more The hydrogen atom as relativistic bound-state system of a proton and an electron in the complex-mass scheme is investigated. Interaction of a proton and an electron in the atom is described by the Lorentz-scalar Coulomb potential; the proton structure is taken into account. The concept of position dependent particle mass is developed. Relativistic wave equation for two interacting spinless particles is derived; asymptotic method is used to solve the equation. % Asymptotic solution of the equation for the system in the form of %standing wave and eigenmasses of the $H$ atom are obtained. Complex eigenmasses for the $H$ atom are obtained. The spin center-of-gravity energy levels for the $H$ atom are calculated and compared with ones obtained from solution of some known relativistic wave equations % the Shrodinger, Klein-Gordon and tabulated NIST data.
Spinless Salpeter equation for two bound particles is analyzed. We use the fact that in relativis... more Spinless Salpeter equation for two bound particles is analyzed. We use the fact that in relativistic kinematics the spatial two particle relative momentum is relativistic invariant. Free particle hypothesis for the bound state is developed: comstituents move as free particles inside of the system. The Shr\"odinger-type wave equation is derived. Three equivalent forms of the eigenvalue equation are given. Relative motion of quarks in eigen states is described by the asymptotic solution in the form of the standing wave of $\cos(kx+a)$ for each spatial degree of freedom. To test the model the spin center-of-gravity energy levels for the hydrogen atom are calculated and compared with the NIST data. Complex eigenmasses for the $H$ atom are obtained.
Mesons containing light and heavy quarks are studied. Interaction of quarks is described by the f... more Mesons containing light and heavy quarks are studied. Interaction of quarks is described by the funnel-type potential with the distant dependent strong coupling, $\alpha_\S(r)$. Free particle hypothesis for the bound state is developed: quark and antiquark move as free particles in of the bound system. Relativistic two-body wave equation with position dependent particle masses is used to describe the flavored $Qq$ systems. Solution of the equation for the system in the form of a~standing wave is given. Interpolating complex-mass formula for two exact asymptotic eigenmass expressions is obtained. Mass spectra for some leading-state flavored mesons are calculated.
Mesons as bound states of quark and anti-quark in the framework of a relativistic potential model... more Mesons as bound states of quark and anti-quark in the framework of a relativistic potential model are studied. Interaction of constituents in bound state is described by the Lorentz-scalar QCD inspired funnel-type potential with the coordinate dependent strong coupling, {\alpha}S(r). Lagrangian relativistic mechanics is used to derive the main dynamic two particle equation of motion. On this basis, relativistic two body wave equation is derived. Solution of the equation for the system in the form of a standing wave is obtained. Two exact asymptotic expressions for the meson squared mass are obtained and used to derive the meson universal mass formula. Light and heavy meson mass spectra are calculated.
ABSTRACT A two-component model to analyze both soft and hard hadronic processes at high energies ... more ABSTRACT A two-component model to analyze both soft and hard hadronic processes at high energies is suggested. The model is based on the topological 1/N expansion of the scattering amplitude and the theory of the supercritical Pomeron. The longitudinal component is given by the string model and determines the behavior of the cross section on longitudinal variables. The dependence on the transverse momentum is calculated on the basis of a two-gluon Pomeron model in which the Pomeron is modeled as an exchange of two nonperturbative gluons whose propagator is finite at q2=0. Hard scattering of quarks on the ends of quark-gluon strings is calculated as a sequence of multi-Pomeron exchanges. It is shown that the propagator which vanishes as (q2)-3 or faster allows one to reproduce hard distributions of secondary hadrons. The model is used to analyze the inclusive spectra of hadrons on the Feynman variable xF and transverse momentum p⊥ up to 10 GeV/c in a wide energy interval.
The properties of relativistic particles in the quasiclassical region are investigated. The relat... more The properties of relativistic particles in the quasiclassical region are investigated. The relativistic semiclassical wave equation appropriate in the quasiclassical region is derived. It is shown that the leading-order WKB quantization rule is the appropriate method to solve the equation obtained.
Anyonic atom is considered as a two-dimensional system. Using some approximations we find the ene... more Anyonic atom is considered as a two-dimensional system. Using some approximations we find the energy spectrum of the anyon in the Coulomb field. It is shown that the anyonic atom is stable.
Three-dimensional Schrödinger's equation is analyzed with the help of the correspondence prin... more Three-dimensional Schrödinger's equation is analyzed with the help of the correspondence principle between classical and quantum-mechanical quantities. Separation is performed after reduction of the original equation to the form of the classical Hamilton–Jacobi equation. Each one-dimensional equation obtained after separation is solved by the conventional WKB method. Quasiclassical solution of the angular equation results in the integral of motion [Formula: see text] and the existence of nontrivial solution for the angular quantum number l = 0. Generalization of the WKB method for multi-turning-point problems is given. Exact eigenvalues for solvable and some "insoluble" spherically symmetric potentials are obtained. Quasiclassical eigenfunctions are written in terms of elementary functions in the form of a standing wave.
The exactness of the semiclassical method for three-dimensional problems in quantum mechanics is ... more The exactness of the semiclassical method for three-dimensional problems in quantum mechanics is analyzed. The wave equation appropriate in the quasiclassical region is derived. It is shown that application of the standard leading-order WKB quantization condition to this equation reproduces exact energy eigenvalues for all solvable spherically symmetric potentials.
The classical limit of wave quantum mechanics is analyzed. It is shown that the basic requirement... more The classical limit of wave quantum mechanics is analyzed. It is shown that the basic requirements of continuity and finiteness to the solution of the form ψ(x) = Aei ϕ (x) + Be-i ϕ (x), where [Formula: see text] and W(x) is the reduced classical action of the physical system, give the asymptote of the wave equation and general quantization condition for the action W(x), which yields the exact eigenvalues of the system.
Physical properties of the Cornell potential in the complex-mass scheme are investigated. Two exa... more Physical properties of the Cornell potential in the complex-mass scheme are investigated. Two exact asymptotic solutions of rela tivistic wave equation for the coulombic and linear components of the potential are used to derive the resonance complex-mass for mula. The centered masses and total widths of the leading p-family resonances are calculated.
The hydrogen atom as relativistic two-body problem is considered. Interaction of a proton and an ... more The hydrogen atom as relativistic two-body problem is considered. Interaction of a proton and an electron in the atom is described by the static Lorentz scalar Coulomb potential. Relativistic two-body wave equation is derived. Lagrangian relativistic mechanics is used to derive the two-particle dynamic equation of motion. The proton structure and motion effects are accounted in the calculations. The energy spectrum of the hydrogen atom is calculated and compared with the tabulated NIST data.
Flavored mesons containing quarks of unequal masses are studied. The appropriate tool is the Beth... more Flavored mesons containing quarks of unequal masses are studied. The appropriate tool is the Bethe-Salpeter formalism, but its inherent complexity leads to series of difficulties mostly related to the central role played in it by the relative time or energy. We consider bound states in the spirit of "Constraint Relativistic Quantum Mechanics (RQM)". Interaction of quarks is described by the funnel-type potential with the distant dependent strong coupling, $\alpha_s(r)$. Relativistic bound-state problem is formulated with the use of symmetries, energy-momentum conservation laws in Minkowskiy space. Relativistic two-body wave equation with position dependent particle masses is derived and used to describe the flavored mesons. Free particle hypothesis for the bound state is developed: quark and antiquark move as free particles in of the bound system. Solution of the equation for the system in the form of a~standing wave is given. Interpolating complex-mass formula for two exa...
The hydrogen atom as relativistic bound-state system of a proton and an electron in the complex-m... more The hydrogen atom as relativistic bound-state system of a proton and an electron in the complex-mass scheme is investigated. Interaction of a proton and an electron in the atom is described by the Lorentz-scalar Coulomb potential; the proton structure is taken into account. The concept of position dependent particle mass is developed. Relativistic wave equation for two interacting spinless particles is derived; asymptotic method is used to solve the equation. % Asymptotic solution of the equation for the system in the form of %standing wave and eigenmasses of the $H$ atom are obtained. Complex eigenmasses for the $H$ atom are obtained. The spin center-of-gravity energy levels for the $H$ atom are calculated and compared with ones obtained from solution of some known relativistic wave equations % the Shrodinger, Klein-Gordon and tabulated NIST data.
Spinless Salpeter equation for two bound particles is analyzed. We use the fact that in relativis... more Spinless Salpeter equation for two bound particles is analyzed. We use the fact that in relativistic kinematics the spatial two particle relative momentum is relativistic invariant. Free particle hypothesis for the bound state is developed: comstituents move as free particles inside of the system. The Shr\"odinger-type wave equation is derived. Three equivalent forms of the eigenvalue equation are given. Relative motion of quarks in eigen states is described by the asymptotic solution in the form of the standing wave of $\cos(kx+a)$ for each spatial degree of freedom. To test the model the spin center-of-gravity energy levels for the hydrogen atom are calculated and compared with the NIST data. Complex eigenmasses for the $H$ atom are obtained.
Mesons containing light and heavy quarks are studied. Interaction of quarks is described by the f... more Mesons containing light and heavy quarks are studied. Interaction of quarks is described by the funnel-type potential with the distant dependent strong coupling, $\alpha_\S(r)$. Free particle hypothesis for the bound state is developed: quark and antiquark move as free particles in of the bound system. Relativistic two-body wave equation with position dependent particle masses is used to describe the flavored $Qq$ systems. Solution of the equation for the system in the form of a~standing wave is given. Interpolating complex-mass formula for two exact asymptotic eigenmass expressions is obtained. Mass spectra for some leading-state flavored mesons are calculated.
Mesons as bound states of quark and anti-quark in the framework of a relativistic potential model... more Mesons as bound states of quark and anti-quark in the framework of a relativistic potential model are studied. Interaction of constituents in bound state is described by the Lorentz-scalar QCD inspired funnel-type potential with the coordinate dependent strong coupling, {\alpha}S(r). Lagrangian relativistic mechanics is used to derive the main dynamic two particle equation of motion. On this basis, relativistic two body wave equation is derived. Solution of the equation for the system in the form of a standing wave is obtained. Two exact asymptotic expressions for the meson squared mass are obtained and used to derive the meson universal mass formula. Light and heavy meson mass spectra are calculated.
ABSTRACT A two-component model to analyze both soft and hard hadronic processes at high energies ... more ABSTRACT A two-component model to analyze both soft and hard hadronic processes at high energies is suggested. The model is based on the topological 1/N expansion of the scattering amplitude and the theory of the supercritical Pomeron. The longitudinal component is given by the string model and determines the behavior of the cross section on longitudinal variables. The dependence on the transverse momentum is calculated on the basis of a two-gluon Pomeron model in which the Pomeron is modeled as an exchange of two nonperturbative gluons whose propagator is finite at q2=0. Hard scattering of quarks on the ends of quark-gluon strings is calculated as a sequence of multi-Pomeron exchanges. It is shown that the propagator which vanishes as (q2)-3 or faster allows one to reproduce hard distributions of secondary hadrons. The model is used to analyze the inclusive spectra of hadrons on the Feynman variable xF and transverse momentum p⊥ up to 10 GeV/c in a wide energy interval.
The properties of relativistic particles in the quasiclassical region are investigated. The relat... more The properties of relativistic particles in the quasiclassical region are investigated. The relativistic semiclassical wave equation appropriate in the quasiclassical region is derived. It is shown that the leading-order WKB quantization rule is the appropriate method to solve the equation obtained.
Anyonic atom is considered as a two-dimensional system. Using some approximations we find the ene... more Anyonic atom is considered as a two-dimensional system. Using some approximations we find the energy spectrum of the anyon in the Coulomb field. It is shown that the anyonic atom is stable.
Three-dimensional Schrödinger's equation is analyzed with the help of the correspondence prin... more Three-dimensional Schrödinger's equation is analyzed with the help of the correspondence principle between classical and quantum-mechanical quantities. Separation is performed after reduction of the original equation to the form of the classical Hamilton–Jacobi equation. Each one-dimensional equation obtained after separation is solved by the conventional WKB method. Quasiclassical solution of the angular equation results in the integral of motion [Formula: see text] and the existence of nontrivial solution for the angular quantum number l = 0. Generalization of the WKB method for multi-turning-point problems is given. Exact eigenvalues for solvable and some "insoluble" spherically symmetric potentials are obtained. Quasiclassical eigenfunctions are written in terms of elementary functions in the form of a standing wave.
The exactness of the semiclassical method for three-dimensional problems in quantum mechanics is ... more The exactness of the semiclassical method for three-dimensional problems in quantum mechanics is analyzed. The wave equation appropriate in the quasiclassical region is derived. It is shown that application of the standard leading-order WKB quantization condition to this equation reproduces exact energy eigenvalues for all solvable spherically symmetric potentials.
The classical limit of wave quantum mechanics is analyzed. It is shown that the basic requirement... more The classical limit of wave quantum mechanics is analyzed. It is shown that the basic requirements of continuity and finiteness to the solution of the form ψ(x) = Aei ϕ (x) + Be-i ϕ (x), where [Formula: see text] and W(x) is the reduced classical action of the physical system, give the asymptote of the wave equation and general quantization condition for the action W(x), which yields the exact eigenvalues of the system.
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Papers by Mikhail N Sergeenko