Non-Hermitian matrix description of the PT symmetric anharmonic oscillators

Schroedinger equation H \psi=E \psi with PT - symmetric differential operator H=H(x) = p^2 + a x^4 + i \beta x^3 +c x^2+i \delta x = H^*(-x) on L_2(-\infty,\infty) is re-arranged as a linear algebraic diagonalization at a>0. The proof of this non-variational construction is given. Our Taylor series form of \psi complements and completes the recent terminating solutions as obtained for certain couplings \delta at the less common negative a.Comment: 18 pages, latex, no figures, thoroughly revised (incl. title), J. Phys. A: Math. Gen., to appea

PT symmetric models in more dimensions and solvable square-well versions of their angular Schroedinger equations

For any central potential V in D dimensions, the angular Schroedinger equation remains the same and defines the so called hyperspherical harmonics. For non-central models, the situation is more complicated. We contemplate two examples in the plane: (1) the partial differential Calogero's three-body model (without centre of mass and with an impenetrable core in the two-body interaction), and (2) the Smorodinsky-Winternitz' superintegrable harmonic oscillator (with one or two impenetrable barriers). These examples are solvable due to the presence of the barriers. We contemplate a small complex shift of the angle. This creates a problem: the barriers become "translucent" and the angular potentials cease to be solvable, having the sextuple-well form for Calogero model and the quadruple or double well form otherwise. We mimic the effect of these potentials on the spectrum by the multiple, purely imaginary square wells and tabulate and discuss the result in the first nontrivial double-well case.Comment: 21 pages, 5 figures (see version 1), amendment (a single comment added on p. 7

Study of a class of non-polynomial oscillator potentials

We develop a variational method to obtain accurate bounds for the eigenenergies of H = -Delta + V in arbitrary dimensions N>1, where V(r) is the nonpolynomial oscillator potential V(r) = r^2 + lambda r^2/(1+gr^2), lambda in (-infinity,\infinity), g>0. The variational bounds are compared with results previously obtained in the literature. An infinite set of exact solutions is also obtained and used as a source of comparison eigenvalues.Comment: 16 page

Eigenvalues from power--series expansions: an alternative approach

An appropriate rational approximation to the eigenfunction of the Schr\"{o}dinger equation for anharmonic oscillators enables one to obtain the eigenvalue accurately as the limit of a sequence of roots of Hankel determinants. The convergence rate of this approach is greater than that for a well--established method based on a power--series expansions weighted by a Gaussian factor with an adjustable parameter (the so--called Hill--determinant method)

Pathophysiology of resistant hypertension: The role of sympathetic nervous system

Resistant hypertension (RH) is a powerful risk factor for cardiovascular morbidity and mortality. Among the characteristics of patients with RH, obesity, obstructive sleep apnea, and aldosterone excess are covering a great area of the mosaic of RH phenotype. Increased sympathetic nervous system (SNS) activity is present in all these underlying conditions, supporting its crucial role in the pathophysiology of antihypertensive treatment resistance. Current clinical and experimental knowledge points towards an impact of several factors on SNS activation, namely, insulin resistance, adipokines, endothelial dysfunction, cyclic intermittent hypoxaemia, aldosterone effects on central nervous system, chemoreceptors, and baroreceptors dysregulation. The further investigation and understanding of the mechanisms leading to SNS activation could reveal novel therapeutic targets and expand our treatment options in the challenging management of RH. Copyright © 2011 Costas Tsioufis et al