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    Wyświetlanie 1-8 z 8
    Tytuł:
    Dispersion estimates for spherical Schrödinger equations: the effect of boundary conditions
    Autorzy:
    Holzleitner, M.
    Kostenko, A.
    Teschl, G.
    Powiązania:
    https://bibliotekanauki.pl/articles/255331.pdf
    Data publikacji:
    2016
    Wydawca:
    Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
    Tematy:
    Schrödinger equation
    dispersive estimates
    scattering
    Opis:
    We investigate the dependence of the [formula] dispersive estimates for one-dimensional radial Schrödinger operators on boundary conditions at 0. In contrast to the case of additive perturbations, we show that the change of a boundary condition at zero results in the change of the dispersive decay estimates if the angular momentum is positive, l ∈ (0,1/2). However, for nonpositive angular momenta, l ∈ (—1/2,0], the standard [formula] decay remains true for all self-adjoint realizations.
    Źródło:
    Opuscula Mathematica; 2016, 36, 6; 769-786
    1232-9274
    2300-6919
    Pojawia się w:
    Opuscula Mathematica
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Quaternions and Cauchy Classical Theory of Elasticity
    Autorzy:
    Danielewski, Marek
    Sapa, Lucjan
    Powiązania:
    https://bibliotekanauki.pl/articles/175624.pdf
    Data publikacji:
    2020
    Wydawca:
    Polska Akademia Nauk. Czytelnia Czasopism PAN
    Tematy:
    wave mechanics
    quaternions
    Cauchy model
    elastic solid
    Schrödinger equation
    Opis:
    Developed by French mathematician Augustin-Louis Cauchy, the classical theory of elasticity is the starting point to show the value and the physical reality of quaternions. The classical balance equations for the isotropic, elastic crystal, demonstrate the usefulness of quaternions. The family of wave equations and the diffusion equation are a straightforward consequence of the quaternion representation of the Cauchy model of the elastic solid. Using the quaternion algebra, we present the derivation of the quaternion form of the multiple wave equations. The fundamental consequences of all derived equations and relations for physics, chemistry, and future prospects are presented.
    Źródło:
    Advances in Manufacturing Science and Technology; 2020, 44, 2; 67-70
    0137-4478
    Pojawia się w:
    Advances in Manufacturing Science and Technology
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Analytical solutions of Schrödinger equation with new solvable potential family V(r)=A/r^2-B/r+Cr^(δ+1) via Nikiforov-Uvarov (NU) method
    Autorzy:
    Antia, Akaninyene Daniel
    Akpan, Ita Okon
    Ikot, Akpan Ndem
    Maghsoodi, Elham
    Zarrinkamar, Saber
    Hassanabadi, Hassan
    Powiązania:
    https://bibliotekanauki.pl/articles/763317.pdf
    Data publikacji:
    2015
    Wydawca:
    Uniwersytet Marii Curie-Skłodowskiej. Wydawnictwo Uniwersytetu Marii Curie-Skłodowskiej
    Tematy:
    Schrödinger equation
    Energy eigenvalue
    Eigenfunction
    Diatomic molecules
    Hellmann-Feynmann theorem
    Opis:
    In this paper, we have presented the exact solutions of the Schrödinger equation with the family of potentials V(r)=A/r^2-B/r+Cr^(δ+1). We have obtained the energy eigenvalues and the corresponding wave functions expressed in terms of the associated Laguerre polynomials for  using the Nikiforov-Uvarov (NU) method. The energy levels for each case is computed for diatomic molecules H2, CO, NO and N2  for various values of and . We have also computed the expectation values of, and the Virial theorem using the Hellmann-Feynmann theorem (HFT).
    Źródło:
    Annales Universitatis Mariae Curie-Skłodowska, sectio AAA – Physica; 2015, 70
    0137-6861
    Pojawia się w:
    Annales Universitatis Mariae Curie-Skłodowska, sectio AAA – Physica
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Controllabilty and stability analysis on a group associated with Black-Scholes equation
    Autorzy:
    Tiwari, Archana
    Bhattacharyya, Debanjana
    Pati, K. C.
    Powiązania:
    https://bibliotekanauki.pl/articles/229513.pdf
    Data publikacji:
    2020
    Wydawca:
    Polska Akademia Nauk. Czytelnia Czasopism PAN
    Tematy:
    Black-Scholes equation
    Schrödinger equation
    Lie group
    optimal control
    stability
    numerical integration
    Opis:
    In this paper we have studied the driftless control system on a Lie group which arises due to the invariance of Black-Scholes equation by conformal transformations. These type of studies are possible as Black-Scholes equation can be mapped to one dimensional free Schrödinger equation. In particular we have studied the controllability, optimal control of the resulting dynamics as well as stability aspects of this system. We have also found out the trajectories of the states of the system through two unconventional integrators along with conventional Runge-Kutta integrator.
    Źródło:
    Archives of Control Sciences; 2020, 30, 3; 553-573
    1230-2384
    Pojawia się w:
    Archives of Control Sciences
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Methods of mathematical quantum theory in selected economic models
    Autorzy:
    Schlichtinger, Agnieszka Matylda
    Powiązania:
    https://bibliotekanauki.pl/articles/584928.pdf
    Data publikacji:
    2018
    Wydawca:
    Wydawnictwo Uniwersytetu Ekonomicznego we Wrocławiu
    Tematy:
    Hilbert space
    quaternions
    quaternionic quantum mechanics
    Schrödinger equation
    regression
    expected utility
    Opis:
    The issue of using the physical method in economics is no longer an innovative idea. However, nowadays the methods of mathematical quantum mechanics are also applied to economic sciences. This is the natural result of the fact that as applicable in quantum mechanics, mathematical spaces and tools turn out to be useful in other fields of science. Then it is possible to assume that the problem of the choice of the space is a universal question that is associated not only with mathematics and physics but also with economics or social sciences. In this paper the author considers various formulations of Hilbert space in relation to finite-dimensional quantum mechanics which constitutes a fundament to also apply my outcomes in economics. On the basis of mathematical considerations the author puts forward the hypothesis that the complex Hilbert space is characterized with numerous advantages in relation to its real and quaternionic alternatives.
    Źródło:
    Mathematical Economics; 2018, 14(21); 95-106
    1733-9707
    Pojawia się w:
    Mathematical Economics
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Existence and uniqueness of the solution to the optimal control problem with integral criterion over the entire domain for a nonlinear Schrödinger equation with a special gradient term
    Autorzy:
    Salmanov, Vuqar
    Powiązania:
    https://bibliotekanauki.pl/articles/2050054.pdf
    Data publikacji:
    2020
    Wydawca:
    Polska Akademia Nauk. Instytut Badań Systemowych PAN
    Tematy:
    Schrödinger equation
    optimal control problem
    first variation of the functional
    complex potential
    Opis:
    The paper concerns the optimal control problem with the full-range integral performance criterion for the nonlinear Schrödinger equation with the specific gradient summand and the complex potential when the performance criterion is the full-range integral. In this paper, the existence and uniqueness theorems regarding the solution of the optimal control problem under consideration are proven.
    Źródło:
    Control and Cybernetics; 2020, 49, 3; 277-290
    0324-8569
    Pojawia się w:
    Control and Cybernetics
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Numerical simulation of coupled quantum dots
    Autorzy:
    Machowska-Podsiadło, E.
    Mączka, M.
    Powiązania:
    https://bibliotekanauki.pl/articles/378437.pdf
    Data publikacji:
    2006
    Wydawca:
    Sieć Badawcza Łukasiewicz - Instytut Technologii Elektronowej
    Tematy:
    kropki kwantowe
    równanie Poissona
    równanie Schrodingera
    LDA
    symulacja numeryczna
    quantum dots
    Poisson equation
    Schrödinger equation
    numerical simulation
    Opis:
    In the work we present self-consistent solutions of Poisson and Schrödinger equations which describe electron states in coupled quantum dots. Results for two neighbouring quantum dots formed in an electrostatic way are discussed. Zero-dimensional electron gas is investigated in the structure proposed by Kastner [1] and presented in our earlier works [2-4]. In the work results of simulations performed in three- and two-dimensional space are shown. We included Hartree potential for modeling Coulomb interactions among electrons in the system. We also considered the exchange and correlation potentials which ensured that each discrete energy level was occupied by only one electron. The exchange and correlation potentials were taken into account with the help of the Local Density Approximation (LDA).
    Źródło:
    Electron Technology : Internet Journal; 2005-2006, 37/38, 13; 1-4
    1897-2381
    Pojawia się w:
    Electron Technology : Internet Journal
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    To the synthesis of classical and quantum physic
    Autorzy:
    Etkin, V. A.
    Powiązania:
    https://bibliotekanauki.pl/articles/1177473.pdf
    Data publikacji:
    2018
    Wydawca:
    Przedsiębiorstwo Wydawnictw Naukowych Darwin / Scientific Publishing House DARWIN
    Tematy:
    Schrödinger equation
    nonequilibrium thermodynamics
    photoeffect
    quantum machanics
    quantums of light
    radiation laws
    spectral series
    wave as quantum
    Opis:
    The possibility has been validated to adjust fundamental differences between classical mechanics and quantum mechanics from the position of the wave theory of matter structure. A derivation of the Planck radiation law has been offered proceeding from the assumption the wave is a true quantum of radiation. The principles of photoeffect have been explained from the positions of classical phisycs and supplemented with consideration of the photoelectric yield. The law of forming spectral series has been obtained with no involvement of quantum numbers and no assumption of electron orbit-to-orbit transition. A deterministic derivation of the Schrödinger stationary wave equation has been given as excluding the necessity of its probability interpretation. The possibility has been shown to construct in unified manner mechanics of macro- and microprocesses considering discretness of wave processes.
    Źródło:
    World Scientific News; 2018, 102; 101-115
    2392-2192
    Pojawia się w:
    World Scientific News
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
      Wyświetlanie 1-8 z 8

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