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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Hojman, S. A., & Asenjo, F. A. (2020). Classical and Quantum Dispersion Relations. Phys. Scr., 95(8), 7 pp.
Abstract: It is showed that, in general, classical and quantum dispersion relations are different due to the presence of the Bohm potential. There are exact particular solutions of the quantum (wave) theory which obey the classical dispersion relation, but they differ in the general case. The dispersion relations may also coincide when additional assumptions are made, such as WKB or eikonal approximations, for instance. This general result also holds for non-quantum wave equations derived from classical counterparts, such as in ray and wave optics, for instance. Explicit examples are given for covariant scalar, vectorial and tensorial fields in flat and curved spacetimes.
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Hojman, S. A., & Asenjo, F. A. (2020). Dual wavefunctions in two-dimensional quantum mechanics. Phys. Lett. A, 384(13), 5 pp.
Abstract: It is shown that the Schrodinger equation for a large family of pairs of two-dimensional quantum potentials possess wavefunctions for which the amplitude and the phase are interchangeable, producing two different solutions which are dual to each other. This is a property of solutions with vanishing Bohm potential. These solutions can be extended to three-dimensional systems. We explicitly calculate dual solutions for physical systems, such as the repulsive harmonic oscillator and the two-dimensional hydrogen atom. These dual wavefunctions are also solutions of an analogue optical system in the eikonal limit. In this case, the potential is related to the refractive index, allowing the study of this two-dimensional dual wavefunction solutions with an optical (analogue) system. (C) 2020 Elsevier B.V. All rights reserved.
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Hojman, S. A., Asenjo, F. A., Moya-Cessa, H. M., & Soto-Eguibar, F. (2021). Bohm potential is real and its effects are measurable. Optik, 232, 166341.
Abstract: We analyze Bohm potential effects both in the realms of Quantum Mechanics and Optics, as well as in the study of other physical phenomena described in terms of classical and quantum wave equations. We approach this subject by using theoretical arguments as well as experimental evidence. We find that the effects produced by Bohm potential are both theoretically responsible for the early success of Quantum Mechanics correctly describing atomic and nuclear phenomena and, more recently, by confirming surprising accelerating behavior of free waves and particles experimentally, for instance.
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Hojman, S. J., Moya-Cessa, H. M., Soto-Eguibar, F., & Asenjo, F. A. (2021). Time-dependent harmonic oscillators and SUSY in time domain. Phys. Scr., 96(12), 125218.
Abstract: We show that the time-dependent harmonic oscillator has a repulsive or inverted oscillator as a time domain SUSY-like partner. Examples of several kinds of super-symmetrical time dependent frequency systems are presented.
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Moya-Cessa, H. M., Asenjo, F. A., Hojman, S. A., & Soto-Eguibar, F. (2022). Two-mode squeezed state generation using the Bohm potential. Mod. Phys. Lett. B, 36(09), 2250025.
Abstract: We show that two-mode squeezed vacuum-like states may be engineered in the Bohm-Madelung formalism by adequately choosing the phase of the wave function. The difference between our wave function and the one of the squeezed vacuum states is given precisely by the phase we selected. We would like to stress that the engineering of two-mode vacuum states is possible due to the existence of the Bohm potential, and it is relevant because of its potential use in the propagation of optical fields, where it may render a variety of applications in optics. The approach to generate non-classical states, namely, two-mode squeezed states of a quantum mechanical system is one of the first applications of the Madelung-Bohm formalism.
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Moya-Cessa, H. M., Hojman, S. A., Asenjo, F. A., & Soto-Eguibar, F. (2022). Bohm approach to the Gouy phase shift. Optik, 252, 168468.
Abstract: By adapting the Madelung-Bohm formalism to paraxial wave propagation we show, by using Ermakov-Lewis techniques, that the Gouy phase is related to the form of the phase chosen in order to produce a Gaussian function as a propagated field. For this, we introduce a quantum mechanical invariant, that it is explicitly time dependent. We finally show that the effective Bohm index of refraction generates a GRIN medium that produces the focusing needed for the Gouy phase.
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