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1
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Generalized linear Schrödinger equations and their Darboux transformations

100%
Schulze-Halberg A.
Open Physics
|
2008
|
vol. 6
|
issue 3
654-661
EN
We construct explicit Darboux transformations of arbitrary order for a class of generalized, linear Schrödinger equations. Our construction contains the well-known Darboux transformations for Schrödinger equations with position-dependent mass, Schrödinger equations coupled to a vector potential and Schrödinger equations for weighted energy.
2
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Supersymmetry of time-dependent Schrödinger equations with effective mass

100%
Schulze-Halberg A.
|
EN
We establish the supersymmetry formalism for time-dependent Schrödinger equations with effective mass and show that the corresponding supersymmetric transformations are equivalent to effective mass Darboux transformations
3
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On some hydrodynamical aspects of quantum mechanics

76%
Spera M.
Open Physics
|
2010
|
vol. 8
|
issue 1
42-48
EN
In this note we first set up an analogy between spin and vorticity of a perfect 2d-fluid flow, based on the complex polynomial (i.e. Borel-Weil) realization of the irreducible unitary representations of SU(2), and looking at the Madelung-Bohm velocity attached to the ensuing spin wave functions. We also show that, in the framework of finite dimensional geometric quantum mechanics, the Schrödinger velocity field on projective Hilbert space is divergence-free (being Killing with respect to the Fubini-Study metric) and fulfils the stationary Euler equation, with pressure proportional to the Hamiltonian uncertainty (squared). We explicitly determine the critical points of the pressure of this “Schrödinger fluid”, together with its vorticity, which turns out to depend on the spacings of the energy levels. These results follow from hydrodynamical properties of Killing vector fields valid in any (finite dimensional) Riemannian manifold, of possible independent interest.
4
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The symmetry group of the quantum harmonic oscillator in an electric field

76%
Lejarreta J., Cerveró J.
Open Physics
|
2008
|
vol. 6
|
issue 3
671-684
EN
In this paper we present two results. First, we derive the most general group of infinitesimal transformations for the Schrödinger Equation of the general time-dependent Harmonic Oscillator in an electric field. The infinitesimal generators and the commutation rules of this group are presented and the group structure is identified. From here it is easy to construct a set of unitary operators that transform the general Hamiltonian to a much simpler form. The relationship between squeezing and dynamical symmetries is also stressed. The second result concerns the application of these group transformations to obtain solutions of the Schrödinger equation in a time-dependent potential. These solutions are believed to be useful for describing particles confined in boxes with moving boundaries. The motion of the walls is indeed governed by the time-dependent frequency function. The applications of these results to non-rigid quantum dots and tunnelling through fluctuating barriers is also discussed, both in the presence and in the absence of a time-dependent electric field. The differences and similarities between both cases are pointed out.
5
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Green’s function for an electron model with a plane wave

76%
Ould Lahoucine H., Chetouani L.
Open Physics
|
2009
|
vol. 7
|
issue 1
184-192
EN
The Green function for a Dirac particle subject to a plane wave field is constructed according to the path integral approach and the Barut’s electron model. Then it is exactly determined after having fixed a matrix U chosen so that the equations of motion are those of a free particle, and by using the properties of the plane wave and also with some shifts.
6
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On the role of entanglement in Schrödinger’s cat paradox

64%
Rinner S., Werner E.
Open Physics
|
2008
|
vol. 6
|
issue 1
178-183
EN
In this paper we re-investigate the core of Schrödinger’s “cat paradox”. We argue that one has to distinguish clearly between superpositions of macroscopic cat states |☺〉 + |☹〉 and superpositions of entangled states |☺, ↑〉 + |☹, ↓〉 which comprise both the state of the cat (☺=alive, ☹=dead) and the radioactive substance (↑=not decayed, ↓=decayed). It is shown, that in the case of the cat experiment recourse to decoherence or other mechanisms is not necessary in order to explain the absence of macroscopic superpositions. Additionally, we present modified versions of two quantum optical experiments as experimenta crucis. Applied rigorously, quantum mechanical formalism reduces the problem to a mere pseudo-paradox.
7
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Stochastic quantization method for spinning particles in a gravitational plane wave field

64%
Lehtihet Z., Chetouani L.
Open Physics
|
2008
|
vol. 6
|
issue 2
372-384
EN
The exact and analytic Green functions for spinning relativistic particles in interaction with a gravitational plane wave field are obtained within the Stochastic Quantization Method of Parisi and Wu. We have separated the classical calculations from those related to the quantum fluctuations. The problem has been solved by using a perturbative treatment via the Langevin equation relying on phase and configuration spaces formulation.
8
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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.
9
Content available remote

The propagator for step potential and mass using path decomposition method

64%
Laissaoui A., Chetouani L.
Open Physics
|
2010
|
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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