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The well-known trigonometric Scarf potential is generalized by adding a sinusoidal term and then treated using the Asymptotic Iteration Method (AIM) and the Tridiagonal Representation Approach (TRA). The energy spectrum of the associated bound states is computed. For the AIM, we have improved convergence of the quantization condition that terminates the iterations asymptotically. This is accomplished by looking for the range of initial values of the space variable in the terminating condition that produces stable results (plateau of convergence). We have shown that with increasing iteration, this plateau of convergence grows up rapidly to an optimal iteration number and then shrinks slowly to a point. The value of this point (or points) may depend on the physical parameters. The numerical results have been compared favorably with those resulting from the TRA. [ABSTRACT FROM AUTHOR]

We introduce exactly solvable quantum parametric oscillators, which are generalizations of the quantum problems related with the classical orthogonal polynomials of Hermite, Laguerre, and Jacobi type, introduced in the work of Büyüka, sık et al. [J. Math. Phys. 50, 072102 (2009)]. Quantization of these models with specific damping, frequency, and external forces is obtained using the Wei-Norman Lie algebraic approach. This determines the evolution operator exactly in terms of two linearly independent homogeneous solutions and a particular solution of the corresponding classical equation of motion. Then, time-evolution of wave functions and coherent states are found explicitly. Probability densities, expectation values, and uncertainty relations are evaluated and their properties are investigated under the influence of the external terms. [ABSTRACT FROM AUTHOR]

In this paper, we study Lie super-bialgebra and quantization of the super Virasoro algebra, whose even part is the centerless twisted Heisenberg-Virasoro algebra. By using some Liu-Pei-Zhu's results, we prove that all Lie super-bialgebra structures on the super Virasoro algebra are triangular coboundary. Furthermore, we quantize the super Virasoro algebra by the Drinfel'd twist quantization technique and obtain a class of noncommutative and noncocommutative Hopf superalgebras. [ABSTRACT FROM AUTHOR]

Covariant affine integral quantization of the half-plane is studied and applied to the motion of a particle on the half-line. We examine the consequences of different quantizer operators built from weight functions on the half-plane. To illustrate the procedure, we examine two particular choices of the weight function, yielding thermal density operators and affine inversion, respectively. The former gives rise to a temperature-dependent probability distribution on the half-plane whereas the latter yields the usual canonical quantization and a quasi-probability distribution (affine Wigner function) which is real, marginal in both momentum p and position q. [ABSTRACT FROM AUTHOR]

In this paper, we construct a sheaf-based topos quantum theory. It is well known that a topos quantum theory can be constructed on the topos of presheaves on the category of commutative von Neumann algebras of bounded operators on a Hilbert space. Also, it is already known that quantization naturally induces a Lawvere-Tierney topology on the presheaf topos. We show that a topos quantum theory akin to the presheaf-based one can be constructed on sheaves defined by the quantization-induced Lawvere-Tierney topology. That is, starting from the spectral sheaf as a state space of a given quantum system, we construct sheaf-based expressions of physical propositions and truth objects, and thereby give a method of truth-value assignment to the propositions. Furthermore, we clarify the relationship to the presheaf-based quantum theory. We give translation rules between the sheaf-based ingredients and the corresponding presheaf-based ones. The translation rules have "coarse-graining" effects on the spaces of the presheaf-based ingredients; a lot of different proposition presheaves, truth presheaves, and presheaf-based truth-values are translated to a proposition sheaf, a truth sheaf, and a sheaf-based truth-value, respectively. We examine the extent of the coarse-graining made by translation. [ABSTRACT FROM AUTHOR]

The problem of Dirac particle interacting with Coulomb potential in (2+1) dimensions is formulated in the framework of super-symmetric path integrals where the spin degrees of freedom are described by odd Grassmannian variables. The relative propagator is expressed through Cartesian coordinates in a Hamiltonian form by the use of an adequate transformation. The passage to the polar coordinates permitted us to calculate the fixed energy Green's function and to extract bound states and associating wave functions. [ABSTRACT FROM AUTHOR]

A degenerate dynamical system is characterized by a symplectic structure whose rank is not constant throughout phase space. Its phase space is divided into causally disconnected, nonoverlapping regions in each of which the rank of the symplectic matrix is constant, and there are no classical orbits connecting two different regions. Here the question of whether this classical disconnectedness survives quantization is addressed. Our conclusion is that in irreducible degenerate systems-in which the degeneracy cannot be eliminated by redefining variables in the action-the disconnectedness is maintained in the quantum theory: there is no quantum tunnelling across degeneracy surfaces. This shows that the degeneracy surfaces are boundaries separating distinct physical systems, not only classically, but in the quantum realm as well. The relevance of this feature for gravitation and Chern-Simons theories in higher dimensions cannot be overstated. [ABSTRACT FROM AUTHOR]

This paper is a continuation of our previous paper where the Painlevé-Calogero correspondence has been extended to auxiliary linear problems associated with Painlevé equations. We have proved, for the first five equations from the Painlevé list, that one of the linear problems can be recast in the form of the non-stationary Schrödinger equation whose Hamiltonian is a natural quantization of the classical Calogero-like Hamiltonian for the corresponding Painlevé equation. In the present paper we establish the quantum Painlevé-Calogero correspondence for the most general case, the Painlevé VI equation. We also show how the desired special gauge and the needed choice of variables can be derived starting from the corresponding Schlesinger system with rational spectral parameter. [ABSTRACT FROM AUTHOR]

The Painlevé-Calogero correspondence is extended to auxiliary linear problems associated with Painlevé equations. The linear problems are represented in a new form which has a suggestive interpretation as a 'quantized' version of the Painlevé-Calogero correspondence. Namely, the linear problem responsible for the time evolution is brought into the form of non-stationary Schrödinger equation in imaginary time, ∂tψ=(12 ∂x2+V(x,t))ψ, whose Hamiltonian is a natural quantization of the classical Calogero-like Hamiltonian H=12 p2+V(x,t) for the corresponding Painlevé equation. In present paper, we present explicit constructions for the first five equations from the Painlevé list. [ABSTRACT FROM AUTHOR]