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Sep 18, 2013
09/13

by
A. Ganguly; L. M. Nieto

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Second order supersymmetric approach is taken to the system describing motion of a quantum particle in a potential endowed with position-dependent effective mass. It is shown that the intertwining relations between second order partner Hamiltonians may be exploited to obtain a simple shape-invariant condition. Indeed a novel relation between potential and mass functions is derived, which leads to a class of exactly solvable model. As an illustration of our procedure, two examples are given for...

Source: http://arxiv.org/abs/0707.3624v1

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Sep 23, 2013
09/13

by
K. Bencheikh; L. M. Nieto

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Closed form analytical expressions are obtained for the Wigner transform of the Bloch density matrix and for the Wigner phase space density of a two dimensional harmonically trapped charged quantum gas in a uniform magnetic field of arbitrary strength, at zero and nonzero temperatures. An exact analytic expression is also obtained for the autocorrelation function. The strong magnetic field case, where only few Landau levels are occupied, is also examined, and useful approximate expressions for...

Source: http://arxiv.org/abs/0810.3615v1

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3.0

Jun 27, 2018
06/18

by
M. L. Glasser; L. M. Nieto

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Motivated by current interest in quantum confinement potentials, especially with respect to the Stark spectroscopy of new types of quantum wells, we examine several novel one-dimensional singular oscillators. A Green function method is applied, the construction of the necessary resolvents is reviewed and several new ones are introduced. In addition, previous work on the singular harmonic oscillator model, introduced by Avakian et al. is reproduced to verify the method and results. A novel...

Topic: Quantum Physics

Source: http://arxiv.org/abs/1505.04362

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Sep 18, 2013
09/13

by
O. Rosas-Ortiz; J. Negro; L. M. Nieto

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A relaxed factorization is used to obtain many of the properties obeyed by the confluent hypergeometric functions. Their implications on the analytical solutions of some interesting physical problems are also studied. It is quite remarkable that, although these properties appear frequently in solving the Schroedinger equation, it has been not clear the role they play in describing the physical systems. The main objective of this communication is precisely to throw some light on the subject.

Source: http://arxiv.org/abs/quant-ph/0105091v1

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Sep 19, 2013
09/13

by
A. Ganguly; M. V. Ioffe; L. M. Nieto

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A new quantum model with rational functions for the potential and effective mass is proposed in a stretchable region outside which both are constant. Starting from a generalized effective mass kinetic energy operator the matching and boundary conditions for the envelope wave functions are derived. It is shown that in a mapping to an auxiliary constant-mass Schrodinger picture one obtains one-period ``associated Lame'' well bounded by two delta-wells or delta-barriers depending on the values of...

Source: http://arxiv.org/abs/quant-ph/0610248v1

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Sep 19, 2013
09/13

by
L. M. Nieto; H. C. Rosu; M. Santander

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An old result of A.F. Stevenson [Phys. Rev.} 59, 842 (1941)] concerning the Kepler-Coulomb quantum problem on the three-dimensional (3D) hypersphere is considered from the perspective of the radial Schr\"odinger equations on 3D spaces of any (either positive, zero or negative) constant curvature. Further to Stevenson, we show in detail how to get the hypergeometric wavefunction for the hydrogen atom case. Finally, we make a comparison between the ``space curvature" effects and minimal...

Source: http://arxiv.org/abs/quant-ph/9911010v3

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Sep 22, 2013
09/13

by
B. Mielnik; L. M. Nieto; O. Rosas-Ortiz

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The higher order supersymmetric partners of the Schroedinger's Hamiltonians can be explicitly constructed by iterating a simple finite difference equation corresponding to the Baecklund transformation. The method can completely replace the Crum determinants. Its limiting, differential case offers some new operational advantages.

Source: http://arxiv.org/abs/quant-ph/0004024v1

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Sep 22, 2013
09/13

by
M. L. Glasser; M. Gadella; L. M. Nieto

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We study a one-dimensional singular potential plus three types of regular interactions: constant electric field, harmonic oscillator and infinite square well. We use the Lippman-Schwinger Green function technique in order to search for the bound state energies. In the electric field case the unique bound state coincides with that found in an earlier study as the field is switched off. For non-zero field the ground state is shifted and positive energy ``quasibound states" appear. For the...

Source: http://arxiv.org/abs/0906.5331v1

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Jul 20, 2013
07/13

by
O. Rosas-Ortiz; B Mielnik; L. M. Nieto

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The higher order susy partners of Schroedinger Hamiltonians can be explicitly constructed by iterating a nonlinear difference algorithm coinciding with the Backlund superposition principle used in soliton theory. As an example, it is applied in the construction of new higher order susy partners of the free particle potential, which can be used as a handy tool in soliton theory.

Source: http://arxiv.org/abs/quant-ph/9910009v1

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25

Jul 20, 2013
07/13

by
J. Negro; L. M. Nieto; O. Rosas-Ortiz

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A generalization of the factorization technique is shown to be a powerful algebraic tool to discover further properties of a class of integrable systems in Quantum Mechanics. The method is applied in the study of radial oscillator, Morse and Coulomb potentials to obtain a wide set of raising and lowering operators, and to show clearly the connection that link these systems.

Source: http://arxiv.org/abs/quant-ph/9910038v1

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Sep 20, 2013
09/13

by
A. Ganguly; S. Kuru; J. Negro; L. M. Nieto

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A square potential well with position-dependent mass is studied for bound states. Applying appropriate matching conditions, a transcendental equation is derived for the energy eigenvalues. Numerical results are presented graphically and the variation of the energy of the bound states are calculated as a function of the well-width and mass.

Source: http://arxiv.org/abs/quant-ph/0608102v1

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Sep 19, 2013
09/13

by
B. F. Samsonov; M. L. Glasser; L. M. Nieto

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Time-dependent supersymmetry allows one to delete quasienergy levels for time-periodic Hamiltonians and to create new ones. We illustrate this by examining an exactly solvable model related to the simple harmonic oscillator with a time-varying frequency. For an interesting nonharmonic example we present the change of the Berry phase due to a supersymmetry transformation.

Source: http://arxiv.org/abs/quant-ph/0304144v1

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0.0

Jun 30, 2018
06/18

by
F. Gungor; S Kuru; J. Negro; L. M. Nieto

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Heisenberg-type higher order symmetries are studied for both classical and quantum mechanical systems separable in cartesian coordinates. A few particular cases of this type of superintegrable systems were already considered in the literature, but here they are characterized in full generality together with their integrability properties. Some of these systems are defined only in a region of $\mathbb R^n$, and in general they do not include bounded solutions. The quantum symmetries and...

Topics: Nonlinear Sciences, Mathematics, Exactly Solvable and Integrable Systems, Mathematical Physics

Source: http://arxiv.org/abs/1411.6216

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Sep 22, 2013
09/13

by
L. M. Nieto; A. A. Pecheritsin; Boris F. Samsonov

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The technique of differential intertwining operators (or Darboux transformation operators) is systematically applied to the one-dimensional Dirac equation. The following aspects are investigated: factorization of a polynomial of Dirac Hamiltonians, quadratic supersymmetry, closed extension of transformation operators, chains of transformations, and finally particular cases of pseudoscalar and scalar potentials. The method is widely illustrated by numerous examples.

Source: http://arxiv.org/abs/quant-ph/0307152v1

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Sep 22, 2013
09/13

by
L. M. Nieto; B. F. Samsonov; A. A. Suzko

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The intertwining operator technique is applied to difference Schroedinger equations with operator-valued coefficients. It is shown that these equations appear naturally when a discrete basis is used for solving a multichannel Schroedinger equation. New families of exactly solvable multichannel Hamiltonians are found.

Source: http://arxiv.org/abs/quant-ph/0309039v1

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0.0

Jun 30, 2018
06/18

by
M. Donaire; J. M. Muñoz-Castañeda; L. M. Nieto

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We compute the interaction energies of a two-atom system placed in the middle of a perfectly reflecting planar cavity, in the perturbative regime. Explicit expressions are provided for the van der Waals potentials of two polarisable atomic dipoles as well as for the electrostatic potential of two induced dipoles. For the van der Waals potentials, several scenarios are considered, namely, a pair of atoms in their ground states, a pair of atoms both excited, and a pair of dissimilar atoms with...

Topic: Quantum Physics

Source: http://arxiv.org/abs/1702.00438

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Sep 17, 2013
09/13

by
A. Ballesteros; F. J. Herranz; J. Negro; L. M. Nieto

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The minimal twist map introduced by B. Abdesselam, A. Chakrabarti, R. Chakrabarti and J. Segar (Mod. Phys. Lett. A 14 (1999) 765) for the non-standard (Jordanian) quantum sl(2,R) algebra is used to construct the twist maps for two different non-standard quantum deformations of the (1+1) Schrodinger algebra. Such deformations are, respectively, the symmetry algebras of a space and a time uniform lattice discretization of the (1+1) free Schrodinger equation. It is shown that the corresponding...

Source: http://arxiv.org/abs/math/0007020v1

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19

Sep 18, 2013
09/13

by
P. G. Estevez; S. Kuru; J. Negro; L. M. Nieto

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A class of particular travelling wave solutions of the generalized Benjamin-Bona-Mahony equation is studied systematically using the factorization technique. Then, the general travelling wave solutions of Benjamin-Bona-Mahony equation, and of its modified version, are also recovered.

Source: http://arxiv.org/abs/0707.0760v2

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Sep 22, 2013
09/13

by
M. V. Ioffe; S. Kuru; J. Negro; L . M. Nieto

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A two-dimensional Pauli Hamiltonian describing the interaction of a neutral spin-1/2 particle with a magnetic field having axial and second order symmetries, is considered. After separation of variables, the one-dimensional matrix Hamiltonian is analyzed from the point of view of supersymmetric quantum mechanics. Attention is paid to the discrete symmetries of the Hamiltonian and also to the Hamiltonian hierarchies generated by intertwining operators. The spectrum is studied by means of the...

Source: http://arxiv.org/abs/hep-th/0603005v1

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59

Jul 20, 2013
07/13

by
O. Cornejo-Perez; J. Negro; L. M. Nieto; H. C. Rosu

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Travelling-wave solutions of the standard and compound form of Korteweg-de Vries-Burgers equations are found using factorizations of the corresponding reduced ordinary differential equations. The procedure leads to solutions of Bernoulli equations of nonlinearity 3/2 and 2 (Riccati), respectively. Introducing the initial conditions through an imaginary phase in the travelling coordinate, we obtain all the solutions previously reported, some of them being corrected here, and showing, at the same...

Source: http://arxiv.org/abs/math-ph/0604004v2

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Sep 18, 2013
09/13

by
J. J. Alvarez-Sanchez; J. V. Alvarez-Bravo; L. M. Nieto

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A new quantum architecture for multiplying signed integers is presented based on Booth's algorithm, which is well known in classical computation. It is shown how a quantum binary chain might be encoded by its flank changes, giving the final product in 2's-complement representation.

Source: http://arxiv.org/abs/quant-ph/0611007v1

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31

Sep 18, 2013
09/13

by
M. V. Ioffe; J. Negro; L. M. Nieto; D. N. Nishnianidze

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Supersymmetrical intertwining relations of second order in the derivatives are investigated for the case of supercharges with deformed hyperbolic metric $g_{ik}=diag(1,-a^2)$. Several classes of particular solutions of these relations are found. The corresponding Hamiltonians do not allow the conventional separation of variables, but they commute with symmetry operators of fourth order in momenta. For some of these models the specific SUSY procedure of separation of variables is applied.

Source: http://arxiv.org/abs/hep-th/0606103v1

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30

Jul 20, 2013
07/13

by
M. Gadella; J. Negro; L. M. Nieto; G. Pronko; M. Santander

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We construct the spectrum generating algebra (SGA) for a free particle in the three dimensional sphere $S^3$ for both, classical and quantum descriptions. In the classical approach, the SGA supplies time-dependent constants of motion that allow to solve algebraically the motion. In the quantum case, the SGA include the ladder operators that give the eigenstates of the free Hamiltonian. We study this quantum case from two equivalent points of view.

Source: http://arxiv.org/abs/1007.1423v1

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84

Jul 20, 2013
07/13

by
J. I. Diaz; J. Negro; L. M. Nieto; O. Rosas-Ortiz

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New supersymmetric partners of the modified Poschl-Teller and the Dirac's delta well potentials are constructed in closed form. The resulting one-parametric potentials are shown to be interrelated by a limiting process. The range of values of the parameters for which these potentials are free of singularities is exactly determined. The construction of higher order supersymmetric partner potentials is also investigated.

Source: http://arxiv.org/abs/quant-ph/9910017v1

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Sep 22, 2013
09/13

by
B F Samsonov; M L Glasser; J Negro; L M Nieto

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The potentials for a one dimensional Schroedinger equation that are displaced along the x axis under second order Darboux transformations, called 2-SUSY invariant, are characterized in terms of a differential-difference equation. The solutions of the Schroedinger equation with such potentials are given analytically for any value of the energy. The method is illustrated by a two-soliton potential. It is proven that a particular case of the periodic Lame-Ince potential is 2-SUSY invariant. Both...

Source: http://arxiv.org/abs/quant-ph/0307146v1

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2.0

Jun 27, 2018
06/18

by
M. Gadella; J. Mateos Guilarte; J. M. Munoz-Castaneda; L. M. Nieto

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In this contribution to the study of one dimensional point potentials, we prove that if we take the limit $q\to 0$ on a potential of the type $v_0\delta({y})+{2}v_1\delta'({y})+w_0\delta({y}-q)+ {2} w_1\delta'({y}-q)$, we obtain a new point potential of the type ${u_0} \delta({y})+{2 u_1} \delta'({y})$, when $ u_0$ and $ u_1$ are related to $v_0$, $v_1$, $w_0$ and $w_1$ by a law having the structure of a group. This is the Borel subgroup of $SL_2({\mathbb R})$. We also obtain the non-abelian...

Topics: Quantum Physics, Mathematical Physics, Mathematics, High Energy Physics - Theory

Source: http://arxiv.org/abs/1505.04359