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Asenjo, F. A., & Hojman, S. A. (2017). Class of Exact Solutions for a Cosmological Model of Unified Gravitational and Quintessence Fields. Found. Phys., 47(7), 887–896.
Abstract: A new approach to tackle Einstein equations for an isotropic and homogeneous Friedmann-Robertson-Walker Universe in the presence of a quintessence scalar field is devised. It provides a way to get a simple exact solution to these equations. This solution determines the quintessence potential uniquely and it differs from solutions which have been used to study inflation previously. It relays on a unification of geometry and dark matter implemented through the definition of a functional relation between the scale factor of the Universe and the quintessence field. For a positive curvature Universe, this solution produces perpetual accelerated expansion rate of the Universe, while the Hubble parameter increases abruptly, attains a maximum value and decreases thereafter. The behavior of this cosmological solution is discussed and its main features are displayed. The formalism is extended to include matter and radiation.
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Hojman, S. A., & Asenjo, F. A. (2020). A new approach to solve the one-dimensional Schrodinger equation using a wavefunction potential. Phys. Lett. A, 384(36), 7 pp.
Abstract: A new approach to find exact solutions to one-dimensional quantum mechanical systems is devised. The scheme is based on the introduction of a potential function for the wavefunction, and the equation it satisfies. We recover known solutions as well as to get new ones for both free and interacting particles with wavefunctions having vanishing and non-vanishing Bohm potentials. For most of the potentials, no solutions to the Schrodinger equation produce a vanishing Bohm potential. A (large but) restricted family of potentials allows the existence of particular solutions for which the Bohm potential vanishes. This family of potentials is determined, and several examples are presented. It is shown that some quantum, such as accelerated Airy wavefunctions, are due to the presence of non-vanishing Bohm potentials. New examples of this kind are found and discussed. (C) 2020 Elsevier B.V. All rights reserved.
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Zalaquett, N., Hojman, S. A., & Asenjo, F. A. (2014). Spinning massive test particles in cosmological and general static spherically symmetric spacetimes. Class. Quantum Gravity, 31(8), 21 pp.
Abstract: A Lagrangian formalism is used to study the motion of a spinning massive particle in Friedmann-Robertson-Walker and Godel spacetimes, as well as in a general Schwarzschild-like spacetime and in static spherically symmetric conformally flat spacetimes. Exact solutions for the motion of the particle and general exact expressions for the momenta and velocities are displayed for different cases. In particular, the solution for the motion in spherically symmetric metrics is presented in the equatorial plane. The exact solutions are found using constants of motion of the particle, namely its mass, its spin, its angular momentum, and a fourth constant, which is its energy when the metric is time-independent, and a different constant otherwise. These constants are associated to Killing vectors. In the case of the motion on the Friedmann-Robertson-Walker metric, a new constant of motion is found. This is the fourth constant which generalizes previously known results obtained for spinless particles. In the case of general Schwarzschild-like spacetimes, our results allow for the exploration of the case of the Reissner-Nordstrom-(Anti) de Sitter metric. Finally, for the case of the conformally flat spacetimes, the solution is explicitly evaluated for different metric tensors associated to a universe filled with static perfect fluids and electromagnetic radiation. For some combination of the values of the constants of motion the particle trajectories may exhibit spacelike velocity vectors in portions of the trajectories.
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