Analytic calculation of energies and wave functions of the quartic and pure quartic oscillators

Ground state energies and wave functions of quartic and pure quartic oscillators are calculated by first casting the Schr\"{o}dinger equation into a nonlinear Riccati form and then solving that nonlinear equation analytically in the first iteration of the quasilinearization method (QLM). In the QLM the nonlinear differential equation is solved by approximating the nonlinear terms by a sequence of linear expressions. The QLM is iterative but not perturbative and gives stable solutions to nonlinear problems without depending on the existence of a smallness parameter. Our explicit analytic results are then compared with exact numerical and also with WKB solutions and it is found that our ground state wave functions, using a range of small to large coupling constants, yield a precision of between 0.1 and 1 percent and are more accurate than WKB solutions by two to three orders of magnitude. In addition, our QLM wave functions are devoid of unphysical turning point singularities and thus allow one to make analytical estimates of how variation of the oscillator parameters affects physical systems that can be described by the quartic and pure quartic oscillators.Comment: 8 pages, 12 figures, 1 tabl

Experience with developing antibiotic stewardship programmes in Serbia : potential model for other Balkan countries?

Introduction: Antimicrobial resistance (AMR) and inappropriate use of antibiotics in children are important issues. Consequently, there is a need to develop comprehensive stewardship programmes even in hospitals with limited resources starting with children’s hospitals. Method: Retrospective observational analysis of antimicrobial utilization and resistance patterns over five years in a tertiary care children’s hospital in Serbia. Results: Cumulative AMR decreased but were still high, with high cumulative resistance rates among the most widely used antibiotics in the hospital. Total antibiotic use decreased from 2010 to 2014 although there was still high prescribing of reserved antibiotics. Conclusion: Concerns with inappropriate use, and high resistance rates, among some antibiotics used in the hospital are being used to develop guidance on future antibiotic use in this hospital, building on the recently introduced antibiotic stewardship programme, as well as encourage other hospitals in Serbia to review their policies