Mikhail Sergeenko - Academia.edu (original) (raw)
Papers by Mikhail Sergeenko
The wave equation in quantum mechanics and its general solution in the phase space are obtained.
arXiv: High Energy Physics - Phenomenology, 2020
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, alphas(r)\alpha_s(r)alphas(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...
arXiv: Quantum Physics, 2019
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 HHH atom are obtained. Complex eigenmasses for the HHH atom are obtained. The spin center-of-gravity energy levels for the HHH atom are calculated and compared with ones obtained from solution of some known relativistic wave equations % the Shrodinger, Klein-Gordon and tabulated NIST data.
arXiv: High Energy Physics - Phenomenology, 2019
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)\cos(kx+a)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 HHH atom are obtained.
arXiv: High Energy Physics - Phenomenology, 2019
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, alphaS(r)\alpha_\S(r)alphaS(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 QqQqQq 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.
arXiv: High Energy Physics - Phenomenology, 2017
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.
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.
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.
Physical Review D, 2000
A two-component model to analyze both soft and hard hadronic processes at high energies is sugges... more 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 q 2 ϭ0. 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 (q 2) Ϫ3 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 x F and transverse momentum p Ќ up to 10 GeV/c in a wide energy interval.
Physical Review A, 1996
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.
Modern Physics Letters A, 1997
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.
Modern Physics Letters A, 1997
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.
Modern Physics Letters A, 1998
Quasiclassical solution of the three-dimensional Schrödinger's equation is given. It is shown... more Quasiclassical solution of the three-dimensional Schrödinger's equation is given. It is shown apparently that the exitence of nonzero minimal angular momentum M0=ℏ/2 corresponds to the quantum fluctuations of the angular momentum and contributes to the energy of the ground state.
Modern Physics Letters A, 2000
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.
International Journal of Modern Physics A, 2003
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.
EPL (Europhysics Letters), 2009
Transverse momentum spectra of charmed and beauty mesons produced in protonproton and proton-anti... more Transverse momentum spectra of charmed and beauty mesons produced in protonproton and proton-antiproton collisions at high energies are analyzed within the modified quarkgluon string model (QGSM) including the internal motion of quarks in colliding hadrons. It is shown that this approach can describe rather satisfactorily the experimental data at not large values of the transverse momentum where the NLO QCD calculation has a big uncertainty. We also show that using both the QGSM and the NLO QCD one can describe these data in a wide region of transverse momenta and give some predictions for the future LHC experiments.
EPL (Europhysics Letters), 2010
PACS 12.39.Mk-Glueball and nonstandard multi-quark/gluon states PACS 12.39.Pn-Potential models PA... more PACS 12.39.Mk-Glueball and nonstandard multi-quark/gluon states PACS 12.39.Pn-Potential models PACS 12.40.Nn-Regge theory, duality PACS 12.40.Yx-Hadron mass models and calculations Abstract.-Glueballs are considered to be bound states of constituent gluons. Relativistic wave equation for two massive gluons interacting by the funnel-type potential is analyzed. Using two exact asymptotic solutions of the equation, we derive an interpolating mass formula and calculate glueball masses in agreement with the lattice data. We obtain the complex non-linear Pomeron trajectory, αP (t), in the whole region of t. The real part of the trajectory corresponds to the soft Pomeron, parameters of which are found from the fit of recent HERA data.
Zeitschrift für Physik C Particles and Fields, 1991
The dependence of distribution functions of quarks, antiquarks, diquarks and their fragmentation ... more The dependence of distribution functions of quarks, antiquarks, diquarks and their fragmentation into hadrons on the transverse momentum kt is discussed in the frame of the quark-gluon string model. We then discuss the division of kt between 2n-quark-antiquark chains, or n-pomeron showers. Hadron and hadron-nuclear processes p-p, p-A, K +-p, K +-A are analysed. A strong dependence of the observed values on the number n is derived by this method, which is of special importance for the analysis of hadron-nucleus collisions. Our method is compared with the regular kt division method.
Zeitschrift für Physik C Particles and Fields, 1994
Simple interpolating formula for the square of the quarkonium mass and an analytic expression for... more Simple interpolating formula for the square of the quarkonium mass and an analytic expression for the Regge trajectories e(t) in a whole region of both light and heavy quarkonia are derived on the basis of the consideration of two asymptotics for the QCD inspired interquark potential. The leading trajectory functions obtained level off at-1 fort ~ oo. This asymptotic value of c~(t), e(t)-~-1, implies that the cross section of the form (1-x) 1-2~t), which is predicted by the triple Regge model, behaves like (1-x) 3. Is this to be attributed to the behaviour of the vector meson exchange or is it some hard scattering contribution swamping the Regge contributions? The intercepts and slopes of the leading Regge trajectories %(0, o:~(t), c~,(t) and ~r(t) are calculated.
The wave equation in quantum mechanics and its general solution in the phase space are obtained.
arXiv: High Energy Physics - Phenomenology, 2020
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, alphas(r)\alpha_s(r)alphas(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...
arXiv: Quantum Physics, 2019
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 HHH atom are obtained. Complex eigenmasses for the HHH atom are obtained. The spin center-of-gravity energy levels for the HHH atom are calculated and compared with ones obtained from solution of some known relativistic wave equations % the Shrodinger, Klein-Gordon and tabulated NIST data.
arXiv: High Energy Physics - Phenomenology, 2019
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)\cos(kx+a)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 HHH atom are obtained.
arXiv: High Energy Physics - Phenomenology, 2019
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, alphaS(r)\alpha_\S(r)alphaS(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 QqQqQq 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.
arXiv: High Energy Physics - Phenomenology, 2017
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.
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.
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.
Physical Review D, 2000
A two-component model to analyze both soft and hard hadronic processes at high energies is sugges... more 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 q 2 ϭ0. 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 (q 2) Ϫ3 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 x F and transverse momentum p Ќ up to 10 GeV/c in a wide energy interval.
Physical Review A, 1996
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.
Modern Physics Letters A, 1997
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.
Modern Physics Letters A, 1997
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.
Modern Physics Letters A, 1998
Quasiclassical solution of the three-dimensional Schrödinger's equation is given. It is shown... more Quasiclassical solution of the three-dimensional Schrödinger's equation is given. It is shown apparently that the exitence of nonzero minimal angular momentum M0=ℏ/2 corresponds to the quantum fluctuations of the angular momentum and contributes to the energy of the ground state.
Modern Physics Letters A, 2000
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.
International Journal of Modern Physics A, 2003
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.
EPL (Europhysics Letters), 2009
Transverse momentum spectra of charmed and beauty mesons produced in protonproton and proton-anti... more Transverse momentum spectra of charmed and beauty mesons produced in protonproton and proton-antiproton collisions at high energies are analyzed within the modified quarkgluon string model (QGSM) including the internal motion of quarks in colliding hadrons. It is shown that this approach can describe rather satisfactorily the experimental data at not large values of the transverse momentum where the NLO QCD calculation has a big uncertainty. We also show that using both the QGSM and the NLO QCD one can describe these data in a wide region of transverse momenta and give some predictions for the future LHC experiments.
EPL (Europhysics Letters), 2010
PACS 12.39.Mk-Glueball and nonstandard multi-quark/gluon states PACS 12.39.Pn-Potential models PA... more PACS 12.39.Mk-Glueball and nonstandard multi-quark/gluon states PACS 12.39.Pn-Potential models PACS 12.40.Nn-Regge theory, duality PACS 12.40.Yx-Hadron mass models and calculations Abstract.-Glueballs are considered to be bound states of constituent gluons. Relativistic wave equation for two massive gluons interacting by the funnel-type potential is analyzed. Using two exact asymptotic solutions of the equation, we derive an interpolating mass formula and calculate glueball masses in agreement with the lattice data. We obtain the complex non-linear Pomeron trajectory, αP (t), in the whole region of t. The real part of the trajectory corresponds to the soft Pomeron, parameters of which are found from the fit of recent HERA data.
Zeitschrift für Physik C Particles and Fields, 1991
The dependence of distribution functions of quarks, antiquarks, diquarks and their fragmentation ... more The dependence of distribution functions of quarks, antiquarks, diquarks and their fragmentation into hadrons on the transverse momentum kt is discussed in the frame of the quark-gluon string model. We then discuss the division of kt between 2n-quark-antiquark chains, or n-pomeron showers. Hadron and hadron-nuclear processes p-p, p-A, K +-p, K +-A are analysed. A strong dependence of the observed values on the number n is derived by this method, which is of special importance for the analysis of hadron-nucleus collisions. Our method is compared with the regular kt division method.
Zeitschrift für Physik C Particles and Fields, 1994
Simple interpolating formula for the square of the quarkonium mass and an analytic expression for... more Simple interpolating formula for the square of the quarkonium mass and an analytic expression for the Regge trajectories e(t) in a whole region of both light and heavy quarkonia are derived on the basis of the consideration of two asymptotics for the QCD inspired interquark potential. The leading trajectory functions obtained level off at-1 fort ~ oo. This asymptotic value of c~(t), e(t)-~-1, implies that the cross section of the form (1-x) 1-2~t), which is predicted by the triple Regge model, behaves like (1-x) 3. Is this to be attributed to the behaviour of the vector meson exchange or is it some hard scattering contribution swamping the Regge contributions? The intercepts and slopes of the leading Regge trajectories %(0, o:~(t), c~,(t) and ~r(t) are calculated.