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1
Publication available in full text mode
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Use of Bersons-Kulsh Form Factor of Short-Pulse Approximation in Rydberg-State Physics

100%
Parzyński R., Sobczak M.
Acta Physica Polonica A
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2003
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vol. 103
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issue 1
13-23
EN
The experiments on high Rydberg states interacting with short electromagnetic pulses were hitherto mainly explained by using numerical integration of the time-dependent Schrödinger equation in a restricted state basis. In this study we apply a different approach based on the Bersons-Kulsh analytical form factor of the short-pulse approximation. This analytical approach is shown to well reproduce the recent experimental results and those of numerical integration of the time-dependent Schrödinger equation both in the case of terahertz half-cycle pulses and optical many-cycle pulses. This fact enables a recommendation of the analytical Bersons-Kulsh form factor as an alternative and efficient method of quantum calculations of electromagnetically induced Rydberg state redistribution.
2
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One-Dimensional versus Three-Dimensional Approaches to the Rydberg Wave Packet Dynamics

100%
Kopyciuk T., Parzyński R.
Acta Physica Polonica A
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2006
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vol. 110
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issue 1
41-49
EN
We show that a one-dimensional approximation to a real three-dimensional atom offers good results for a selected group of the Rydberg states. It is demonstrated in the context of evolution of the Rydberg wave packets produced by the so-called half-cycle pulses.
3
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Effective Mass of Bound and Resonant Two-Electron Pairs in a Simple Cubic Lattice

100%
Bak M.
Acta Physica Polonica A
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2015
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vol. 127
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issue 2
290-292
EN
Effective masses m* of bound 2-electron pairs on a simple cubic lattice were investigated within tUWJ model within symmetry channels. Linear increase of m* with |W| for intersite pairs and nonlinear behavior and sign change of m* in case of pairs with on-site component were found. |m*| turned out to be larger than twice free electron mass.
4
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Simplified Solving Procedure for the One-Dimensional Schrodinger Equation with Asymmetrical Boundary Conditions

100%
Puszkarski H.
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vol. 96
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issue 3-4
327-331
EN
We propose a new simplified procedure for finding the analytical solutions of the stationary one-dimensional Schrodinger equation, with asymmetric boundary conditions imposed on the equation. The essence of the method consists in expressing the general solution explicitly in terms of the boundary parameters in a form which, by itself, satisfies one of the boundary conditions involved; then, the other boundary condition gives straightforwardly the characteristic equation. This method may turn out to be beneficial with regard to the recently growing interest in one-dimensional quantum systems.
5
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Bound States of Fermions on 2d Lattice in a Dilute Limit

80%
Bąk M., Micnas R.
Acta Physica Polonica A
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2000
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vol. 97
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issue 1
209-212
EN
We examine extended bound states in a dilute limit of the extended Hubbard model on the two-dimensional square lattice. By solving exactly the two-body problem we have determined the binding energies, mobilities, and dispersion curves across the Brillouin zone for bound states of various symmetries. It turns out that the d-wave pairing is strongly favored by the nnn hopping and the intersite local pairs can have small effective masses, even in the case of strong binding.We have also found a possibility of extended s-d_{x^{2}-y^{2}} mixing of the bound states.
6
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Relativistic Paschen-Back Effect for the Two-Dimensional H-Like Atoms

80%
Poszwa A., Rutkowski A.
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issue 3
439-444
EN
The classification of states based on good quantum numbers for the two-dimensional Coulomb problem is proposed. The first order magnetic energy corrections are calculated using exact field-free analytic solutions of the Dirac equation as a zero-order approximation.
7
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Engineering and Advanced Digitalization of Photonic Structures with Bound Field in the Continuum

80%
Prodanović N., Milanović V., Radovanović J.
Acta Physica Polonica A
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2009
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vol. 116
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issue 4
607-610
EN
We describe a method for generation of complex optical potentials which support a bound state of the electric field in continuous part of the spectrum. It is based on deep analogy between quantum mechanical and electromagnetic phenomena and relies on the application of supersymmetric quantum mechanics to generate a smoothly varying complex optical potential, together with the corresponding electric field function for the (single) localized state. However, the obtained potential profile is generally a strongly oscillating function which requires additional processing to make it suitable for practical realization. With this goal in mind, i.e. the construction of a realizable photonic crystal with complex permittivity which supports one bound state in continuum, we have developed an original scheme of digital grading. It approximates the values of the complex relative permittivity in such manner that the final structure may be realized by assembling layers of homogeneous materials.
8
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Pseudo-Orbit Expansion for the Resonance Condition on Quantum Graphs and the Resonance Asymptotics

80%
Lipovský J.
Acta Physica Polonica A
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2015
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vol. 128
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issue 6
968-973
EN
In this note we explain the method how to find the resonance condition on quantum graphs, which is called pseudo-orbit expansion. In three examples with standard coupling we show in detail how to obtain the resonance condition. We focus on non-Weyl graphs, i.e. the graphs which have fewer resonances than expected. For these graphs we explain benefits of the method of "deleting edges" for simplifying the graph.
9
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Complete Analytical Solutions of the Mie-Type Potentials in N-Dimensions

80%
Agboola D.
Acta Physica Polonica A
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2011
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vol. 120
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issue 3
371-377
EN
The exact solutions of the N-dimensional Schrödinger equation with the Mie-type potentials are obtained. The energy levels are worked out and the corresponding wave functions are obtained in terms of the Laguerre polynomial. Some energy levels of some diatomic molecules are given using the modified Kratzer-type potential. The expectation values 〈r^{-1}〉 and 〈r^{-2}〉 and the virial theorem are also obtained in N-dimensions using the Hellmann-Feynman theorem. The ladder operators are also constructed for the Mie-type potentials in N-dimensions and the matrix elements of some operators r and r·d/dr are analytically obtained from the ladder operators. The general results reduce to the 3-dimensional case when N = 3.
10
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Exact Solutions of Bose-Einstein Condensate in Linear Magnetic Field and Time-Dependent Laser Field

80%
Huang W., Mao J., Qiu W.
Acta Physica Polonica A
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2011
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vol. 119
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issue 3
294-297
EN
A generalized G'/G-expansion method is extended to construct exact solutions for the Gross-Pitaevskii equation with weak bias magnetic and time-dependent laser fields. Many types of exact solutions including hyperbolic function solution, trigonometric function solution and rational exact solution with parameters are obtained. In addition, soliton solutions are found.
11
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Solutions of One-Dimensional Effective Mass Schrödinger Equation for PT-Symmetric Scarf Potential

80%
Zhang A., Shi P., Ling Y., Hua Z.
Acta Physica Polonica A
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2011
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vol. 120
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issue 6
987-991
EN
The one-dimensional effective mass Schrödinger equation for PT-symmetric Scarf potential is investigated. The analytical expressions of energy eigenvalue and corresponding wave function are presented. They are accomplished by using an appropriate coordinate transformation to map the transformed exactly solvable one-dimensional Schrödinger equation with constant mass into the position-dependent mass equation. In the computation, three different forms of mass distributions are considered.
12
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Bound States for Pseudoharmonic Potential of the Dirac Equation with Spin and Pseudo-Spin Symmetry via Laplace Transform Approach

80%
Biswas B., Debnath S.
Acta Physica Polonica A
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2016
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vol. 130
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issue 3
692-696
EN
Bound state solutions of the Dirac equation for the pseudoharmonic potential with spin and pseudo-spin symmetry are studied in this paper. To obtain the exactly normalized bound state wave function and energy expressions we have used the Laplace transform approach.
13
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Adiabatic Processes in Quantum Optics

80%
Stenholm S.
Acta Physica Polonica A
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2002
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vol. 101
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issue 3
425-435
EN
This paper reviews the use of adiabatic approximations in quantum optics.The general principle is explained in terms of the Landau-Zener model and the recently developed stimulated Raman adiabatic passage scheme. The features characteristic of adiabatic evolution are extracted from these examples. Our recent work on adiabatic level preparation and cavity mode transfer of excitation is presented and discussed.
14
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Exact Solutions and Light Bullet Soliton Solutions of the Two-Dimensional Generalized Nonlinear Schrödinger Equation with Distributed Coefficients

80%
Huang W., Mu C., Xu Y., Ding B.
Acta Physica Polonica A
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2013
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vol. 124
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issue 4
622-625
EN
A generalized G'/G-expansion method is extended to construct exact solutions to the two-dimensional generalized nonlinear Schrödinger equation with distributed coefficients. Hyperbolic function solution, trigonometric function solution and rational exact solution with parameters are obtained. Selecting parameters and parameter functions properly, novel light bullet soliton solutions with or without the chirp are presented.
15
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Approximate Solutions of Schrödinger Equation under Manning-Rosen Potential in Arbitrary Dimension via SUSYQM

80%
Hassanabadi H., Lu L., Zarrinkamar S., Liu G., Rahimov H.
Acta Physica Polonica A
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2012
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vol. 122
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issue 4
650-654
EN
The Schrödinger equation under the Manning-Rosen potential is solved in arbitrary dimension via the quantum mechanical idea of supersymmetry. The Pekeris approximation is used to overcome the inconsistency of the potential with the centrifugal term. Comments on the energy eigenvalue behavior versus dimension are included. The inter-dimensional degeneracy for various orbital quantum number l and dimensions D are studied. The expectation values of some physical parameters are reported via the Feynman-Hellmann theorem.
16
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S-Wave Bound- and Resonant States of Two Fermions in Simple Cubic Lattice

80%
Bak M.
Acta Physica Polonica A
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2012
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vol. 121
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issue 4
808-811
EN
Resonant two-electron states are examined in attractive Hubbard model on simple cubic lattice and exact formula for scattering cross section in the limit of low density (empty lattice) is calculated. S-wave pair is considered by means of lattice Green functions (LGF). Analytical form of these functions found by Joyce is used facilitating calculations, which were greatly hindered before by the necessity of using LGF's tabulated values. It is found that the actual peak of scattering cross-section is formed on the lower band boundary in discrepancy with formulae of the theory of scattering in solids.
17
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The Relativistic Transmission and Reflection Coefficients for Woods-Saxon Potential

80%
Yazarloo B., Mehraban H.
Acta Physica Polonica A
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2016
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vol. 129
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issue 6
1089-1092
EN
The relativistic problem of spin-1/2 particles subject to the Woods-Saxon potential is investigated by using the functional analysis method. We obtain scattering and bound state solutions of the one-dimensional Dirac equation with the Woods-Saxon potential in terms of the Jacobi polynomials. We also calculated the transmission and reflection coefficients by using behavior of the wave functions at infinity.
18
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Semiclassical Double-Inequality on Heisenberg Uncertainty Relation in 1D

80%
Bering K.
Acta Physica Polonica A
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2016
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vol. 129
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issue 6
1093-1099
EN
We prove a double-inequality for the product of uncertainties for position and momentum of bound states for 1D quantum mechanical systems in the semiclassical limit.
19
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Asymptotics of Resonances Induced by Point Interactions

80%
Lipovský J., Lotoreichik V.
Acta Physica Polonica A
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2017
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vol. 132
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issue 6
1677-1682
EN
We consider the resonances of the self-adjoint three-dimensional Schrödinger operator with point interactions of constant strength supported on the set X={xₙ}_{n=1}^{N}. The size of X is defined by V_{X} = max_{π ∈ Π_{N}} ∑_{n=1}^{N} |xₙ - x_{π(n)}|, where Π_{N} is the family of all the permutations of the set {1,2,...,N}. We prove that the number of resonances counted with multiplicities and lying inside the disc of radius R behaves asymptotically linear W_{X}/πR + O(1) as R → ∞, where the constant W_{X} ∈ [0,V_{X}] can be seen as the effective size of X. Moreover, we show that there exist a configuration of any number of points such that W_{X}=V_{X}. Finally, we construct an example for N=4 with W_{X} < V_{X}, which can be viewed as an analogue of a quantum graph with non-Weyl asymptotics of resonances.
20
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Dirac-Deng-Fan Problem with Coulomb-Hulthen Tensor Interactions

80%
Ikot A., Hassanabadi H., Yazarloo B., Umo M., Zarrinkamar S.
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vol. 126
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issue 3
656-662
EN
The relativistic symmetries of the Dirac equation within the framework of spin and pseudospin symmetries is investigated for Deng-Fan potential including the Coulomb-like and Hulthen-type potential tensor interaction terms. The energy eigenvalues and the corresponding wave function are obtained using the parametric generalization of Nikiforov-Uvarov method. We have also reported some numerical results and figures to show the effect of the tensor interactions.
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