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  1. 8 Open Physics
  2. 4 Przegląd Elektrotechniczny
  3. 2 Journal of Applied Analysis
  4. 2 Nanoscale Systems: Mathematical Modeling, Theory and Applications
  5. 1 Advances in Manufacturing Science and Technology
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  1. 1 2022
  2. 1 2021
  3. 4 2020
  4. 3 2018
  5. 1 2017
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  1. 7 Mączka M.
  2. 4 Pawłowski S.
  3. 3 Machowska-Podsiadło E.
  4. 2 Bhattacharyya D.
  5. 2 Bugajski M.
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1
Content available remote The Cauchy problem for the nonlinear Schrödinger equations involving derivative terms in one spatial dimension
100%
Baoxiang W.
Annales Societatis Mathematicae Polonae. Seria 1: Commentationes Mathematicae
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2003
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tom [Z] 43(2)
275-300
EN
This paper is devoted to the study of the Cauchy problem for the nonlinear Schrödinger equations involving derivative terms. By introducing a generalized gauge transformation, we give some sufficient conditions for the global well-posedness of solutions in the energy space.
2
Content available remote Exact solution of D-dimensional Schrödinger equation generated from certain central power-law potentials
100%
Bhagawati N.
Open Physics
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2014
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tom 12
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nr 4
256-265
EN
By applying Extended Transformation method we have generated exact solution of D-dimensional radial Schrödinger equation for a set of power-law multi-term potentials taking singular potentials $$V(r) = ar^{ - \tfrac{1} {2}} + br^{ - \tfrac{3} {2}}$$, $$V(r) = ar^{\tfrac{2} {3}} + br^{ - \tfrac{2} {3}} + cr^{ - \tfrac{4} {3}}$$, V(r) = ar + br −1 + cr 2 and V(r) = ar 2+br −2+cr −4+dr −6 as input reference. The restriction on the parameters of the given potentials and angular momentum quantum number ℓ are obtained. The multiplet structure of the generated exactly solvable potentials are also shown.
3
Content available remote Nonlinear stability analysis of electrified liquid jet under the influence of a uniform axial periodic electric field
80%
Mahmoud Y. D.
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2000
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tom Vol. 4, nr 2
251--267
EN
The parametric excitation of surface waves on a liquid jet in the presence of an axial periodic electric field is investigated . The method of multiple scales is used to derive and analyze the necessary and sufficient conditions for stability. Owing to the periodicity, resonant cases appear .Two parametrically nonlinear Schrodinger equations are obtained for the resonance cases . The formula for the surface elevation is derived in each case . A classical nonlinear Schrődinger equation is deduced for the non -resonance case . Investigation of the stability criterion by nonlinear perturbation shows that the periodic electric field has a stabilizing effect.
4
Content available remote A Note on Optimal Control Problem Governed by Schrödinger Equation
80%
Koçak Y. , Çelik E. , Aksoy N. Y.
Open Physics
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2015
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tom 13
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nr 1
EN
In this work, we present some results showing the controllability of the linear Schrödinger equation with complex potentials. Firstly we investigate the existence and uniqueness theorem for solution of the considered problem. Then we find the gradient of the cost functional with the help of Hamilton-Pontryagin functions. Finally we state a necessary condition in the form of variational inequality for the optimal solution using this gradient.
5
Content available 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
80%
Salmanov V.
Control and Cybernetics
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2020
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tom Vol. 49, No. 3
277--290
EN
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.
6
Content available remote Numerical Solution via Numerov Method of the 1D-Schrödinger Equation with Pseudo-Delta Barrier
80%
Martinz S. D. G. , Ramos R. V.
Computational Methods in Science and Technology
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2018
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tom Vol. 24, No. 3
177--185
EN
In this work, aiming to solve numerically the Schrödinger equation with a Dirac delta function potential, we use the Numerov method to solve the time independent 1D-Schrödinger equation with potentials of the form V (x) + αβp(x), where δp(x) is a pseudo-delta function, a very high and thin barrier. The numerical results show good agreement with analytical results found in the literature. Furthermore, we show the numerical solutions of a system formed by three delta function potentials inside of an infinite quantum well and the harmonic potential with position dependent mass and a delta barrier in the center.
7
Content available Dispersion estimates for spherical Schrödinger equations: the effect of boundary conditions
80%
Holzleitner M. , Kostenko A. , Teschl G.
Opuscula Mathematica
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2016
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tom Vol. 36, no. 6
769--786
EN
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.
8
Content available remote On the origin of space
80%
Herrmann R.
Open Physics
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2013
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tom 11
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nr 10
1212-1220
EN
Within the framework of fractional calculus with variable order the evolution of space in the adiabatic limit is investigated. Based on the Caputo definition of a fractional derivative using the fractional quantum harmonic oscillator a model is presented, which describes space generation as a dynamic process, where the dimension d of space evolves smoothly with time in the range 0 ≤ d(t) ≤ 3, where the lower and upper boundaries of dimension are derived from first principles. It is demonstrated, that a minimum threshold for the space dimension is necessary to establish an interaction with external probe particles. A possible application in cosmology is suggested.
9
Content available remote Quantum optimal control using the adjoint method
80%
Borzì A.
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2012
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tom 1
93-111
EN
Control of quantum systems is central in a variety of present and perspective applications ranging from quantum optics and quantum chemistry to semiconductor nanostructures, including the emerging fields of quantum computation and quantum communication. In this paper, a review of recent developments in the field of optimal control of quantum systems is given with a focus on adjoint methods and their numerical implementation. In addition, the issues of exact controllability and optimal control are discussed for finite- and infinitedimensional quantum systems. Some insight is provided considering ’two-level’ models. This work is completed with an outlook to future developments.
10
Content available remote Calculation method for the continuum states of atomic systems
70%
Nikolopoulos L.
Open Physics
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2013
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tom 11
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nr 9
1074-1081
EN
In the present work, we develop a calculational method of solving the scattering equations for spherically symmetric potentials by expanding the solutions on Coulomb functions. We utilize a multistep integration scheme together with the standard partial wave analysis in a region where the potential term dominates. The method applies to any physical problem expressed as [∇ 2 + V(r) + k 2]ψ(r) = 0, while the extension of the method to more general scattering problems is briefly discussed. At present, we demonstrate a two-step Coulomb-fitted integration scheme by calculating the short-range scattering phase shifts for various potentials V (r).
11
Content available 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
70%
Antia A. D. , Akpan I. O. , Ikot A. N. , Maghsoodi E. , Zarrinkamar S. , Hassanabadi H.
|
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tom 70
EN
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).
12
On some non-Gaussian wave packets
70%
Patkowski A. E.
Journal of Applied Analysis
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2018
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tom Vol. 24, nr 1
109--114
EN
We expand on a previous study by offering a generalized wave function associated with the parabolic cylinder function and a connection with a two-particle position-space wave function. We also provide an explicit formula for a wave function associated with a recent work by the present author and M. Wolf.
13
On integrals associated with the free particle wave packet
70%
Patkowski A. E.
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2020
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tom Vol. 26, nr 2
257--262
EN
We discuss some properties of integrals associated with the free particle wave packet, ψ(x, t), which are solutions to the time-dependent Schrödinger equation for a free particle. Some noteworthy discussion is made in relation to integrals which have appeared in the literature. We also obtain formulas for half-integer arguments of the Riemann zeta function.
14
Content available remote On solutions of the Schrödinger equation for some molecular potentials: wave function ansatz
60%
Ikhdair S. , Sever R.
|
|
tom 6
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nr 3
697-703
EN
Making an ansatz to the wave function, the exact solutions of the D-dimensional radial Schrödinger equation with some molecular potentials, such as pseudoharmonic and modified Kratzer, are obtained. Restrictions on the parameters of the given potential, δ and ν are also given, where η depends on a linear combination of the angular momentum quantum number ℓ and the spatial dimensions D and δ is a parameter in the ansatz to the wave function. On inserting D = 3, we find that the bound state eigensolutions recover their standard analytical forms in literature.
15
Content available remote Effect of the velocity-dependent potentials on the energy eigenvalues of the Morse potential
60%
Soylu A. , Bayrak O. , Boztosun I.
Open Physics
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2012
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tom 10
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nr 4
953-959
EN
We investigate the effect of the isotropic velocity-dependent potentials on the bound state energy eigenvalues of the Morse potential for any quantum states. When the velocity-dependent term is used as a constant parameter, ρ(r) = ρ 0, the energy eigenvalues can be obtained analytically by using the Pekeris approximation. When the velocity-dependent term is considered as an harmonic oscillator type, ρ(r) = ρ 0 r 2, we show how to obtain the energy eigenvalues of the Morse potential without any approximation for any n and ℓ quantum states by using numerical calculations. The calculations have been performed for different energy eigenvalues and different numerical values of ρ 0, in order to show the contribution of the velocity-dependent potential on the energy eigenvalues of the Morse potential.
16
Content available remote Analityczno-numeryczna metoda badania właściwości stanów kwantowych w supersieciach półprzewodnikowych
60%
Pawłowski S. , Mączka M.
Przegląd Elektrotechniczny
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2017
|
tom R. 93, nr 12
139--142
PL
W artykule przedstawiono efektywną, pół-analityczną metodę samouzgodnionionego rozwiązywania równań Schrödingera i Poissona w supersieciach półprzewodnikowych. Bazuje ona na aproksymacji funkcji gęstości ładunku wielomianami, co pozwala uzyskać analityczne rozwiązania w/w równań oraz zastosować metodę macierzy przejścia.
EN
The paper presents an efficient, semi-analytical method of self-consistent solution of Schrödinger and Poisson equations in semiconductor superlatices. It is based on the approximation of electrical charge density function by polynomial. This allows us to obtain the analytical solutions of the above-mentioned equations and to apply the Transfer Matrix Formulation (TMF).
17
Content available Methods of mathematical quantum theory in selected economic models
60%
Schlichtinger A. M.
Mathematical Economics
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2018
|
nr 14(21)
95-106
EN
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.
18
Content available remote Shape-invariant hypergeometric type operators with application to quantum mechanics
60%
Cotfas N.
Open Physics
|
2006
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tom 4
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nr 3
318-330
EN
A hypergeometric type equation satisfying certain conditions defines either a finite or an infinite system of orthogonal polynomials. The associated special functions are eigenfunctions of some shape-invariant operators. These operators can be analysed together and the mathematical formalism we use can be extended in order to define other shape-invariant operators. All the shape-invariant operators considered are directly related to Schrödinger-type equations.
19
Content available remote Hybrid fluid-quantum coupling for the simulation of the transport of partially quantized particles in a DG-MOSFET
60%
Jourdana C. , Vauchelet N.
|
|
tom 4
|
nr 1
EN
This paper is devoted to numerical simulations of electronic transport in nanoscale semiconductor devices forwhich charged carriers are extremely confined in one direction. In such devices, like DG-MOSFETs, the subband decomposition method is used to reduce the dimensionality of the problem. In the transversal direction electrons are confined and described by a statistical mixture of eigenstates of the Schrödinger operator. In the longitudinal direction, the device is decomposed into a quantum zone (where quantum effects are expected to be large) and a classical zone (where they are negligible). In the largely doped source and drain regions of a DG-MOSFET, the transport is expected to be highly collisional; then a classical transport equation in diffusive regime coupled with the subband decomposition method is used for the modeling, as proposed in N. Ben Abdallah et al. (2006, Proc. Edind. Math. Soc. [7]). In the quantum region, the purely ballistic model presented in Polizzi et al. (2005, J. Comp. Phys. [25]) is used. This work is devoted to the hybrid coupling between these two regions through connection conditions at the interfaces. These conditions have been obtained in order to verify the continuity of the current. A numerical simulation for a DG-MOSFET, with comparison with the classical and quantum model, is provided to illustrate our approach.
20
Content available Controllabilty and stability analysis on a group associated with Black-Scholes equation
60%
Tiwari A. , Bhattacharyya D. , Pati K. C. , Tiwari A. , Bhattacharyya D. , Pati K. C.
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