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Wyświetlanie 1-15 z 21
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:
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:
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
Tytuł:
Electron dynamics in a strong laser field with Gaussian Potential well
Autorzy:
Gunatilaka, C. C.
Gamalath, K. A. I. L. Wijewardena
Powiązania:
https://bibliotekanauki.pl/articles/1191504.pdf
Data publikacji:
2016
Wydawca:
Przedsiębiorstwo Wydawnictw Naukowych Darwin / Scientific Publishing House DARWIN
Tematy:
Helium-Neon
Ti-Sapphire
time dependant Schrodinger equation
Strong laser field
Gaussian potential well
Argon
Opis:
The time dependant Schrodinger equation was solved for one dimensional and two dimensional Gaussian potential wells in the presence of a strong laser field. Three laser fields Argon, Helium-Neon and Ti-Sapphire with different intensities with cosine and sine laser electric fields were used for the simulation. The Gaussian potential well get distorted in two different ways with the intensity change and the wavelength change of the laser. The wave functions and the position probabilities are presented. The Gaussian potential distortion for He-Ne laser occur in the opposite way compared to Ar and Ti-Sapphire for cosine electric field while Ar laser behaves differently than He-Ne and Ti-Sapphire for sine electric field of the laser in the case of two dimensional potential.
Źródło:
World Scientific News; 2016, 40; 264-283
2392-2192
Pojawia się w:
World Scientific News
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Cubic nonlinear fractional Schrödinger equation with conformable derivative and its new travelling wave solutions
Autorzy:
Gündoğdu, Hami
Gözükızıl, Ömer Faruk
Powiązania:
https://bibliotekanauki.pl/articles/1839843.pdf
Data publikacji:
2021
Wydawca:
Politechnika Częstochowska. Wydawnictwo Politechniki Częstochowskiej
Tematy:
cubic nonlinear fractional Schrödinger equation
travelling wave solutions
kink solution
soliton solution
równanie różniczkowe zwyczajne
roztwór solitonu
równanie Schrödingera
fale biegnące
Opis:
In the present paper, the fractional-order cubic nonlinear Schrödinger equation is considered. The Schrödinger equation with time and space fractional derivative is studied at the same time. Different types of travelling wave solutions including the kink solution, soliton solution, periodic solution, and singular solution for the mentioned equation are obtained by using the Jacobi elliptic functions expansion method. It is shown that the solutions turn into the exact solutions when the fractional orders go to 1. This method can be relied on gaining the solutions to time or space fractional order partial differential equations as well as ordinary ones. Throughout this work, the fractional derivative is given in a conformable sense.
Źródło:
Journal of Applied Mathematics and Computational Mechanics; 2021, 20, 1; 29-41
2299-9965
Pojawia się w:
Journal of Applied Mathematics and Computational Mechanics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Controllable propagation of Pearcey–Gaussian beams in photorefractive media with fractional Schrödinger equation
Autorzy:
Guo, Teng
Gao, Ru
Ren, Shumin
Wang, Pengxiang
Xiao, Yan
Powiązania:
https://bibliotekanauki.pl/articles/2172852.pdf
Data publikacji:
2022
Wydawca:
Politechnika Wrocławska. Oficyna Wydawnicza Politechniki Wrocławskiej
Tematy:
Pearcey-Gaussian beam
fractional Schrödinger equation
photorefractive medium
breathing soliton
Opis:
Taking the fractional Schrödinger equation as the theoretical model, the evolution behavior of the Pearcey–Gaussian beam in the photorefractive medium is studied. The results show that breathing solitons are generated when the nonlinear effect and the diffraction effect are balanced with each other. Nonlinear coefficients, Lévy index and beams amplitude affect breathing period of the soliton and maximum peak intensity. Within a certain range, the breathing period of the soliton decreases with the increase of the nonlinear coefficient and the Lévy index. However when the beams amplitude increases, the breathing period and the maximum peak intensity of the soliton increase. Under the photorefractive effect, due to the bidirectional self-acceleration property of the Pearcey beam, the solitons formed will propagate vertically. These properties can be used to manipulate the beam and have potential applications in optical switching, plasma channeling, particle manipulation, etc.
Źródło:
Optica Applicata; 2022, 52, 4; 627--638
0078-5466
1899-7015
Pojawia się w:
Optica Applicata
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Global well-posedness and scattering for the focusing nonlinear Schrödinger equation in the nonradial case
Autorzy:
Han, P.
Powiązania:
https://bibliotekanauki.pl/articles/254861.pdf
Data publikacji:
2012
Wydawca:
Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
Tematy:
critical energy
focusing Schrodinger equation
global well-posedness
scattering
Opis:
The energy-critical, focusing nonlinear Schrödinger equation in the nonradial case reads as follows: [formula]. Under a suitable assumption on the maximal strong solution, using a compactness argument and a virial identity, we establish the global well-posedness and scattering in the nonradial case, which gives a positive answer to one open problem proposed by Kenig and Merle [Invent. Math. 166 (2006), 645-675].
Źródło:
Opuscula Mathematica; 2012, 32, 3; 487-504
1232-9274
2300-6919
Pojawia się w:
Opuscula Mathematica
Dostawca treści:
Biblioteka Nauki
Artykuł
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:
Efficient computation of the MCTDHF approximation to the time-dependent Schrodinger equation
Autorzy:
Koch, O.
Powiązania:
https://bibliotekanauki.pl/articles/255895.pdf
Data publikacji:
2006
Wydawca:
Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
Tematy:
multi-configuration time-dependent Hartree-Fock method
time-dependent multi-particle Schrodinger equation
Coulomb potential
finite elements
Opis:
We discuss analytical and numerical properties of the multi-configuration time-dependent Hartree-Fock method for the approximate solution of the time-dependent multi-particle (electronic) Schrödinger equation which are relevant for an efficient implementation of this model reduction technique. Particularly, we focus on a discretization and Iow rank approximation in the evaluation of the meanfield terms occurring in the MCTDHF equations of motion, which is crucial for the computational tractability of the problem. We give error bounds for this approximation and demonstrate the achieved gain in performance.
Źródło:
Opuscula Mathematica; 2006, 26, 3; 483-497
1232-9274
2300-6919
Pojawia się w:
Opuscula Mathematica
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Strzałka czasu a niektóre interpretacje mechaniki kwantowej
Time Arrow and Some Interpretations Of Quantum Mechanics
Autorzy:
Łagosz, Marek
Powiązania:
https://bibliotekanauki.pl/articles/2013391.pdf
Data publikacji:
2006
Wydawca:
Katolicki Uniwersytet Lubelski Jana Pawła II. Towarzystwo Naukowe KUL
Tematy:
strzałka czasu
EPR-eksperyment
równanie Schrödingera
(a)symetria czasowa
niezmienniczość względem odwrócenia czasu
pomiar kwantowy
parametry ukryte
time arrow
EPR-experiment
Schrödinger’s equation
time (a)symetry
time- reversal invariance
quantal measurements
“hidden variables”
Opis:
In the paper I discuss some premises of “quantum mechanics” with regard to the thesis that the time arrow does (not) exist. In this context I consider above all the famous Einstein-Podolsky-Rosen’s experiment (EPR-experiment). I also indicate Schrödinger’s interpretation of wave function “symmetrical” towards time (nomological isotropy) and the peculiar understanding of the pair particle-antiparticle, assuming that the direction of time can be reversed. Eventually, I discuss the issue of measurement in quantum mechanics with which the existence of time arrow (anisotropy) is often linked. If it comes to the interpretations of quantum mechanics, from the point of which I consider the issues in question, then in principle I limit myself to two: the so-called Copenhagen interpretation and David Bohm’s conception of “hidden parameters.” I arrive at a conclusion that the premises of quantum mechanics that are at issue here cannot be sufficient grounds for a conclusive recognition of the reversibility (non-existence) of time arrow.
Źródło:
Roczniki Filozoficzne; 2006, 54, 2; 391-411
0035-7685
Pojawia się w:
Roczniki Filozoficzne
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:
Modulational instability of obliquely interacting capillary-gravity waves over infinite depth
Autorzy:
Manna, S.
Dhar, A. K.
Powiązania:
https://bibliotekanauki.pl/articles/38629088.pdf
Data publikacji:
2021
Wydawca:
Instytut Podstawowych Problemów Techniki PAN
Tematy:
nonlinear Schrödinger equation
crossing sea states
capillary-gravity waves
modulational instability
Opis:
Two coupled time-dependent two dimensional nonlinear Schrödinger equations have been derived using multiscale expansion for two nonlinearly interacting capillary-gravity waves over an infinite depth of water. These equations are then utilised to discuss the modulational (Benjamin-Feir) instability of two Stokes wavetrains due to unidirectional and bidirectional perturbations. It is found from the graphs and the three-dimensional contour plots that the rate of growth of instability for two wave packets interacting obliquely is higher than the instance of modulation of one wave packet. We have likewise examined the influence of capillarity on modulational instability.
Źródło:
Archives of Mechanics; 2021, 73, 5-6; 583-598
0373-2029
Pojawia się w:
Archives of Mechanics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
An Axiomatic Approach to Quantum Mechanics
Autorzy:
Rajakaruna, M. A. I. S.
Wijewardena Gamalath, K. A. I. L.
Powiązania:
https://bibliotekanauki.pl/articles/1076342.pdf
Data publikacji:
2019
Wydawca:
Przedsiębiorstwo Wydawnictw Naukowych Darwin / Scientific Publishing House DARWIN
Tematy:
Du Bois Raymond Lemma
Fisher Information
Quantum Mechanics
Schrödinger’s Wave Equation
Variational Principle
Opis:
We have shown that the Schrödinger wave equation can be explained and derived from fundamental postulates that are based on the conservation of probability, significance of measurements at infinity and nature’s tendency of maintaining a system as unbiased as possible. As a reasonable measure for the local randomness, Fisher information is considered. The presented approach provides an axiomatic derivation for the Schrödinger wave equation, avoiding imperfect models borrowed from classical mechanics such as direct application of the energy conservation, statistical mechanics or vibrating string models.
Źródło:
World Scientific News; 2019, 116; 209-221
2392-2192
Pojawia się w:
World Scientific News
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Initial value problem for the time-dependent linear Schrodinger equation with a point singular potential by the unified transform method
Autorzy:
Rybalko, Y.
Powiązania:
https://bibliotekanauki.pl/articles/255033.pdf
Data publikacji:
2018
Wydawca:
Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
Tematy:
Fokas unified transform method Schrodinger equation
interface problem
Opis:
We study an initial value problem for the one-dimensional non-stationary linear Schrodinger equation with a point singular potential. In our approach, the problem is considered as a system of coupled initial-boundary value (IBV) problems on two half-lines, to which we apply the unified approach to IBV problems for linear and integrable nonlinear equations, also known as the Fokas unified transform method. Following the ideas of this method, we obtain the integral representation of the solution of the initial value problem.
Źródło:
Opuscula Mathematica; 2018, 38, 6; 883-898
1232-9274
2300-6919
Pojawia się w:
Opuscula Mathematica
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
Wyświetlanie 1-15 z 21

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