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1
Content available remote

On uncertainty relations in noncommutative phase space

100%
Guo G., Long C., Qin S.
Open Physics
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2010
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vol. 8
|
issue 1
126-130
EN
The uncertainty relations are discussed on a noncommutative plane when noncommutativity of momentum spaces is considered. It is possible to construct normalizable states by simultaneously saturating two coordinate-momentum uncertainty relations. However, under the natural condition θη ≪ 4ħ2 one can not construct a normalizable state by simultaneously saturating any other pairs out of four basic nontrivial uncertainty relations.
2
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A concise quantum mechanical treatment of the forced damped harmonic oscillator

100%
Li T.
Open Physics
|
2008
|
vol. 6
|
issue 4
891-894
EN
By selecting a right generalized coordinate X, which contains the general solutions of the classical motion equation of a forced damped harmonic oscillator, we obtain a simple Hamiltonian which does not contain time for the oscillator such that Schrödinger equation and its solutions can be directly written out in X representation. The wave functin in x representation are also given with the help of the eigenfunctions of the operator $$ \hat X $$ in x representation. The evolution of $$ \left\langle {\hat x} \right\rangle $$ is the same as in the classical mechanics, and the uncertainty in position is independent of an external influence; one part of energy mean is quantized and attenuated, and the other is equal to the classical energy.
3
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Approximate analytical solution of continuous states for the l-wave Schrödinger equation with a diatomic molecule potential

100%
Wei G.-F., Qiang W.-C., Chen W.-L.
Open Physics
|
2010
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vol. 8
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issue 4
574-579
EN
The continuous states of the l-wave Schrödinger equation for the diatomic molecule represented by the hyperbolical function potential are carried out by a proper approximation scheme to the centrifugal term. The normalized analytical radial wave functions of the l-wave Schrödinger equation for the hyperbolical function potential are presented and the corresponding calculation formula of phase shifts is derived. Also, we interestingly obtain the corresponding bound state energy levels by analyzing analytical properties of scattering amplitude.
4
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Particle tunneling and scattering in a three-dimensional potential with a barrier

100%
Olkhovsky V., Petrillo V., Jakiel J., Kantor W.
Open Physics
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2008
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vol. 6
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issue 1
122-127
EN
The particle tunneling through a 3-D rectangular potential barrier has been studied. The simplest model for multiple internal reflections has been assumed. The explicit expression for all the transmission and reflection probability amplitudes have been derived, as well as the tunneling and reflection phase times.
5
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Gazeau-Klauder type coherent states for hypergeometric type operators

100%
Cotfas N.
Open Physics
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2009
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vol. 7
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issue 1
147-159
EN
Hypergeometric type operators are shape invariant, and a factorization into a product of first order differential operators can be explicitely described in the general case. Some additional shape invariant operators depending on several parameters are defined in a natural way by starting from this general factorization. The mathematical properties of the eigenfunctions and eigenvalues of the operators thus obtained depend on the values of the parameters involved. We study the parameter dependence of orthogonality, square integrability and monotony of the eigenvalue sequence. The results obtained allow us to define certain systems of Gazeau-Klauder type coherent states and to describe some of their properties. Our systematic study recovers a number of well-known results in a natural, unified way and also leads to new findings.
6
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The asymptotic iteration method applied to certain quasinormal modes and non Hermitian systems

100%
Özer O., Roy P.
Open Physics
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2009
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vol. 7
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issue 4
747-752
EN
We study the Schrödinger equation with potentials admitting quasinormal modes using the asymptotic iteration method (AIM). We also study non-Hermitian PT symmetric potentials using AIM. The spectra, in all cases, are found to be in excellent agreement with exact results.
7
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On solutions of the Schrödinger equation for some molecular potentials: wave function ansatz

76%
Ikhdair S., Sever R.
Open Physics
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2008
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vol. 6
|
issue 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.
8
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Relativistic solution in D-dimensions to a spin-zero particle for equal scalar and vector ring-shaped Kratzer potential

76%
Ikhdair S., Sever R.
Open Physics
|
2008
|
vol. 6
|
issue 1
141-152
EN
The Klein-Gordon equation in D-dimensions for a recently proposed ring-shaped Kratzer potential is solved analytically by means of the conventional Nikiforov-Uvarov method. The exact energy bound states and the corresponding wave functions of the Klein-Gordon are obtained in the presence of the non-central equal scalar and vector potentials. The results obtained in this work are more general and can be reduced to the standard forms in three dimensions given by other works.
9
Content available remote

Long time properties of the evolution of an unstable state

76%
Urbanowski K.
Open Physics
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2009
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vol. 7
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issue 4
696-703
EN
An effect generated by the nonexponential behavior of the survival amplitude of an unstable state in the long time region is considered. In 1957 Khalfin proved that this amplitude tends to zero as t → ∞ more slowly than any exponential function of t. This can be described in terms of the time-dependent decay rate γ(t) which, when considered with the Khalfin result, means that this γ(t) is not a constant for large t but that it tends to zero as t → ∞. We find that a similar conclusion can be drawn for a large class of models of unstable states for a quantity, which can be interpreted as the “instantaneous energy” of the unstable state. This energy should be much smaller for suitably larger values of t than when t is of the order of the lifetime of the considered state. Within a given model we show that the energy corrections in the long (t → ∞) and relatively short (lifetime of the state) time regions, are different. This is a purely quantum mechanical effect. It is hypothesized that there is a possibility to detect this effect by analyzing the spectra of distant astrophysical objects. The above property of unstable states may influence the measured values of astrophysical and cosmological parameters.
10
Content available remote

Exactly solvable problems of quantum mechanics and their spectrum generating algebras: A review

76%
Rasinariu C., Mallow J., Gangopadhyaya A.
Open Physics
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2007
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vol. 5
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issue 2
111-134
EN
In this review, we summarize the progress that has been made in connecting supersymmetry and spectrum generating algebras through the property of shape invariance. This monograph is designed to be used by our fellow researchers, by other interested physicists, and by students at the graduate and even undergraduate levels who would like a brief introduction to the field.
11
Content available remote

On Generalized Landau Levels

76%
Krasoń P., Milewski J.
Acta Physica Polonica A
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2017
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vol. 132
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issue 1
94-96
EN
We consider the dispersion of energy levels for both standard and inverted quantum harmonic oscillators in the presence of a uniform electromagnetic field. For this analysis we use a solution of the corresponding eigenproblem in terms of the Kummer functions. We find a complete description of the energy levels for a particle of mass m and electric charge q subject to the action of a harmonic oscillator and simultaneous uniform magnetic and electric fields. We also analyze the effect of spin on energy levels for an electron.
12
Content available remote

Exact solutions of the radial Schrödinger equation for some physical potentials

76%
Ikhdair S., Sever R.
|
EN
By using an ansatz for the eigenfunction, we have obtained the exact analytical solutions of the radial Schrödinger equation for the pseudoharmonic and the Kratzer potentials in two dimensions. The bound-state solutions are easily calculated from this eigenfunction ansatz. The corresponding normalized wavefunctions are also obtained.
13
Content available remote

Application of asymptotic iteration method to the Khare-Mandal and its PT-symmetric QES partner potential

76%
Özer O., Aslan V.
Open Physics
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2008
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vol. 6
|
issue 4
879-883
EN
We study the application of the asymptotic iteration method to the Khare-Mandal potential and its PT-symmetric partner. The eigenvalues and eigenfunctions for both potentials are obtained analytically. We have shown that although the quasi-exactly solvable energy eigenvalues of the Khare-Mandal potential are found to be in complex conjugate pairs for certain values of potential parameters, its PT-symmetric partner exhibits real energy eigenvalues in all cases.
14
Content available remote

Exact solutions of the D-dimensional Schrödinger equation for a ring-shaped pseudoharmonic potential

64%
Ikhdair S., Sever R.
Open Physics
|
2008
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vol. 6
|
issue 3
685-696
EN
A new non-central potential, consisting of a pseudoharmonic potential plus another recently proposed ring-shaped potential, is solved. It has the form $$ V(r,\theta ) = \tfrac{1} {8}\kappa r_e^2 \left( {\tfrac{r} {{r_e }} - \tfrac{{r_e }} {r}} \right)^2 + \tfrac{{\beta cos^2 \theta }} {{r^2 sin^2 \theta }} $$. The energy eigenvalues and eigenfunctions of the bound-states for the Schrödinger equation in D-dimensions for this potential are obtained analytically by using the Nikiforov-Uvarov method. The radial and angular parts of the wave functions are obtained in terms of orthogonal Laguerre and Jacobi polynomials. We also find that the energy of the particle and the wave functions reduce to the energy and the wave functions of the bound-states in three dimensions.
15
Content available remote

Approximate analytical solutions of the generalized Woods-Saxon potentials including the spin-orbit coupling term and spin symmetry

64%
Ikhdair S., Sever R.
Open Physics
|
2010
|
vol. 8
|
issue 4
652-666
EN
We study the approximate analytical solutions of the Dirac equation for the generalized Woods-Saxon potential with the pseudo-centrifugal term. We apply the Nikiforov-Uvarov method (which solves a second-order linear differential equation by reducing it to a generalized hypergeometric form) to spin- and pseudospin-symmetry to obtain, in closed form, the approximately analytical bound state energy eigenvalues and the corresponding upper- and lower-spinor components of two Dirac particles. The special cases κ = ±1 (s = $$ \tilde l $$ = 0, s-wave) and the non-relativistic limit can be reached easily and directly for the generalized and standard Woods-Saxon potentials. We compare the non-relativistic results with those obtained by others.
16
Content available remote

Coherent states for Smorodinsky-Winternitz potentials

64%
Ünal N.
Open Physics
|
2009
|
vol. 7
|
issue 4
774-785
EN
In this study, we construct the coherent states for a particle in the Smorodinsky-Winternitz potentials, which are the generalizations of the two-dimensional harmonic oscillator problem. In the first case, we find the non-spreading wave packets by transforming the system into four oscillators in Cartesian, and also polar, coordinates. In the second case, the coherent states are constructed in Cartesian coordinates by transforming the system into three non-isotropic harmonic oscillators. All of these states evolve in physical-time. We also show that in parametric-time, the second case can be transformed to the first one with vanishing eigenvalues.
17
Content available remote

The propagator for step potential and mass using path decomposition method

64%
Laissaoui A., Chetouani L.
Open Physics
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2010
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vol. 8
|
issue 4
562-573
EN
The one-dimensional path decomposition expression for the step potential and mass is formulated. The propagator is analytically determined and the limiting case m 1; m 2 → m is exactly obtained.
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