sh(2/2) Superalgebra eigenstates and generalized supercoherent and supersqueezed states

The superalgebra eigenstates (SAES) concept is introduced and then applied to find the SAES associated to the $sh(2/2)$ superalgebra, also known as Heisenberg--Weyl Lie superalgebra. This implies to solve a Grassmannian eigenvalue superequation. Thus, the $sh(2/2)$ SAES contain the class of supercoherent states associated to the supersymmetric harmonic oscillator and also a class of supersqueezed states associated to the osp(2/2) \sdir sh(2/2) superalgebra, where $osp(2/2)$ denotes the orthosymplectic Lie superalgebra generated by the set of operators formed from the quadratic products of the Heisenberg--Weyl Lie superalgebra generators. The properties of these states are investigated and compared with those of the states obtained by applying the group-theoretical technics. Moreover, new classes of generalized supercoherent and supersqueezed states are also obtained. As an application, the superHermitian and $\eta$--pseudo--superHermitian Hamiltonians without a defined Grassmann parity and isospectral to the harmonic oscillator are constructed. Their eigenstates and associated supercoherent states are calculated.Comment: 42 page

Nonclassical States for Non-Hermitian Hamiltonians with the Oscillator Spectrum

In this paper, we show that the standard techniques that are utilized to study the classical-like properties of the pure states for Hermitian systems can be adjusted to investigate the classicality of pure states for non-Hermitian systems. The method is applied to the states of complex-valued potentials that are generated by Darboux transformations and can model both non-PT-symmetric and PT-symmetric oscillators exhibiting real spectra.MINECO project MTM2014- 57129-C2-1-P, and Junta de Castilla y León project VA057U16

Classical ladder functions for Rosen-Morse and curved Kepler-Coulomb systems

Producción CientíficaLadder functions in classical mechanics are defined in a similar way as ladder operators in the context of quantum mechanics. In the present paper, we develop a new method for obtaining ladder functions of one dimensional systems by means of a product of two ‘factor functions’. We apply this method to the curved Kepler–Coulomb and Rosen–Morse II systems whose ladder functions were not found yet. The ladder functions here obtained are applied to get the motion of the systems.Ministerio de Economía, Industria y Competitividad (project MTM2014-57129-C2-1-P)Junta de Castilla y León-FEDER (projects BU229P18 / VA057U16 / VA137G18)

Coherent states for a generalization of the harmonic oscillator

Coherent states for a family of isospectral oscillator Hamiltonians are derived from a suitable choice of annihilation and creation operators. The Fock-Bargmann representation is also obtained

Multicohort analysis of the maternal age effect on recombination

Several studies have reported that the number of crossovers increases with maternal age in humans, but others have found the opposite. Resolving the true effect has implications for understanding the maternal age effect on aneuploidies. Here, we revisit this question in the largest sample to date using single nucleotide polymorphism (SNP)-chip data, comprising over 6,000 meioses from nine cohorts. We develop and fit a hierarchical model to allow for differences between cohorts and between mothers. We estimate that over 10 years, the expected number of maternal crossovers increases by 2.1% (95% credible interval (0.98%, 3.3%)). Our results are not consistent with the larger positive and negative effects previously reported in smaller cohorts. We see heterogeneity between cohorts that is likely due to chance effects in smaller samples, or possibly to confounders, emphasizing that care should be taken when interpreting results from any specific cohort about the effect of maternal age on recombination

Generalized and Gaussian coherent states for the Morse potential

In this paper, we consider the one-dimensional anharmonic oscillator, which represents well the anharmonic vibrations in diatomic molecules. For the description of the associate potential we use the Morse potential, which gives a good approximation of the experimentally observed vibrational modes of molecules and hence contributes to the realistic description of the spectrum of diatomic molecules. The generalized and Gaussian coherent states are thus constructed and compared in terms of the localization of the particle in those states. We apply these results to the example of the sodium chloride molecule, 1H35Cl

Squeezed coherent states and the one-dimensional Morse quantum system

Abstract The Morse potential one-dimensional quantum system is a realistic model for studying vibrations of atoms in a diatomic molecule. This system is very close to the harmonic oscillator one. We thus propose a construction of squeezed coherent states similar to the one of the harmonic oscillator using ladder operators. The properties of these states are analysed with respect to the localization in position, minimal Heisenberg uncertainty relation, the statistical properties and illustrated with examples using the finite number of states in a well-known diatomic molecule. This article is part of a special issue of Journal of Physics A: Mathematical and Theoretical devoted to 'Coherent states: mathematical and physical aspects'

Trajectories of generalized quantum states for systems with finite discrete spectrum and classical analogs

In this paper, we construct generalized quantum states for systems with finite discrete spectrum and compare the behavior of those states with the classical analogs. Phase-space trajectories are analyzed in the classical and quantum cases. We focus on the following bounded anharmonic exactly solvable one-dimensional potentials: Morse, hyperbolic Pöschl-Teller and Rosen-Morse