Methods for Cancellation of Apparent Cerenkov Radiation Arising From SME Models and Separability of Schrödinger’s Equation Using Exotic Potentials in Parabolic Coordinates

In an attempt to merge the two prominent areas of physics: The Standard Model and General Relativity, there have been many theories for the underlying physics that may lead to Lorentz- and CPT-symmetry violations. At the present moment, technology allows numerous types of Planck-sensitive tests of these symmetries in a range of physical systems. We address a curiosity in isotropic CPT- and Lorentz-violating electrodynamics where there is a kinematic allowance for Cerenkov radiation of a charged particle in a vacuum moving with uniform motion. This however, should not be the case as it is known that constant motion in a vacuum should not cause the particle to lose any energy. Taking Fourier transforms of the modified magnetic field confirms the cancellation of the apparent radiation. The Fourier transform can be used to show that modes for short and long wavelengths cancel. In the second area of research we focus on solutions of the Schrödinger equation which may be found by separation of variables in more than one coordinate system. This class of potentials includes a number of important examples, including the isotropic harmonic oscillator and the Coulomb potential. There are multiple separable Hamiltonians that exhibit a number of interesting features, including “accidental” degeneracies in their bound state spectra and often classical bound state orbits that always close. We examine another potential, for which the Schrödinger equation is separable in both cylindrical and parabolic coordinates: a z-independent V ∝ 1/p2 = 1/ (x2 + y2) in three dimensions. All the persistent, bound classical orbits in this potential close, because all other orbits with negative energies fall to the center at ρ = 0. When separated in parabolic coordinates, the Schrödinger equation splits into three individual equations, two of which are equivalent to the radial equation in a Coulomb potential—one equation with an attractive potential, the other with an equally strong repulsive potential

Separability of the Planar 1/ρ21/\rho^{2} Potential In Multiple Coordinate Systems

With a number of special Hamiltonians, solutions of the Schr\"{o}dinger equation may be found by separation of variables in more than one coordinate system. The class of potentials involved includes a number of important examples, including the isotropic harmonic oscillator and the Coulomb potential. Multiply separable Hamiltonians exhibit a number of interesting features, including "accidental" degeneracies in their bound state spectra and often classical bound state orbits that always close. We examine another potential, for which the Schr\"{o}dinger equation is separable in both cylindrical and parabolic coordinates: a $z$-independent $V\propto 1/\rho^{2}=1/(x^{2}+y^{2})$ in three dimensions. All the persistent, bound classical orbits in this potential close, because all other orbits with negative energies fall to the center at $\rho=0$. When separated in parabolic coordinates, the Schr\"{o}dinger equation splits into three individual equations, two of which are equivalent to the radial equation in a Coulomb potential---one equation with an attractive potential, the other with an equally strong repulsive potential.Comment: 18 page

Mode Analysis for Energetics of a Moving Charge in Lorentz- and CPT -Violating Electrodynamics

In isotropic but Lorentz- and CPT -violating electrodynamics, it is known that a charge in uniform motion does not lose any energy to Cerenkov radiation. This presents a puzzle, since the radiation appears to be kinematically allowed for many modes. Studying the Fourier transforms of the most important terms in the modified magnetic field and Poynting vector, we confirm the vanishing of the radiation rate. Moreover, we show that the Fourier transform of the field changes sign between small and large wave numbers. This enables modes with very long wavelengths to carry negative energies, which cancel out the positive energies carried away by modes with shorter wavelengths. This cancelation had previously been inferred but never explicitly demonstrated

Mode Analysis for Energetics of a Moving Charge In Lorentz- and CPT-Violating Electrodynamics

In isotropic but Lorentz- and CPT-violating electrodynamics, it is known that a charge in unifom motion does not lose any energy to Cerenkov radiation. This presents a puzzle, since the radiation appears to be kinematically allowed for many modes. Studying the Fourier transforms of the most important terms in the modified magnetic field and Poynting vector, we confirm the vanishing of the the radiation rate. Moreover, we show that the Fourier transform of the field changes sign between small and large wave numbers. This enables modes with very long wavelengths to carry negative energies, which cancel out the positive energies carried away by modes with shorter wavelengths. This cancelation had previously been inferred but never explicitly demonstrated.Comment: 16 page

Maternal 'near miss' collection at an Australian tertiary maternity hospital

Background: Australia has a maternal mortality ratio of 6.8/100000 live births, a rate akin to other developed countries and consistent with the high level care provided within the Australian health care system. With maternal mortality at very low levels assessment of severe maternal morbidity is increasingly being used as an indicator of quality of care and to identify areas for improvement in maternity services. The WHO maternal 'near miss' criteria is a standardised tool has been increasingly used worldwide to assess maternal morbidity and standards of maternity care. The aim of this study was to determine the rate and aetiology of maternal 'near misses' at King Edward Memorial Hospital (KEMH) using the WHO near miss criteria. Methods: Cases of maternal 'near miss' were prospectively identified at KEMH using the WHO near miss criteria over a period of 6 months (1st December 2014 to 31st May 2015). A descriptive analysis of the results was undertaken. Results: During the study there were 2773 live births with 19 women who had 'near miss' presentations. There were no maternal deaths. The maternal 'near miss' index rate was 7/1000 live births. The main causes of obstetric 'near miss' were obstetric haemorrhage, pre-eclampsia and early pregnancy complications. Conclusion: The rate of maternal 'near miss' at KEMH was 7/1000 live births and post-partum haemorrhage was identified as the most common aetiology, consistent with other studies in developed countries. Further research comparing currently utilised local, state and national morbidity systems would allow further validation of the WHO near miss criteria in Australian settings

Mode Analysis for Energetics of a Moving Charge In Lorentz- and CPT-Violating Electrodynamics

In isotropic but Lorentz- and CPT-violating electrodynamics, it is known that a charge in uniform motion does not lose any energy to Cerenkov radiation. This presents a puzzle, since the radiation appears to be kinematically allowed for many modes. Studying the Fourier transforms of the most important terms in the modified magnetic field and Poynting vector, we confirm the vanishing of the radiation rate. Moreover, we show that the Fourier transform of the field changes sign between small and large wave numbers. This enables modes with very long wavelengths to carry negative energies, which cancel out the positive energies carried away by modes with shorter wavelengths. This cancelation had previously been inferred but never explicitly demonstrated

Separability of the Planar 1/ρ\u3csup\u3e2\u3c/sup\u3e Potential in Multiple Coordinate Systems

With a number of special Hamiltonians, solutions of the Schrödinger equation may be found by separation of variables in more than one coordinate system. The class of potentials involved includes a number of important examples, including the isotropic harmonic oscillator and the Coulomb potential. Multiply separable Hamiltonians exhibit a number of interesting features, including “accidental” degeneracies in their bound state spectra and often classical bound state orbits that always close. We examine another potential, for which the Schrödinger equation is separable in both cylindrical and parabolic coordinates: A z-independent V/ρ2=1/(x2+y2) in three dimensions. All the persistent, bound classical orbits in this potential close, because all other orbits with negative energies fall to the center at ρ=0. When separated in parabolic coordinates, the Schrödinger equation splits into three individual equations, two of which are equivalent to the radial equation in a Coulomb potential—one equation with an attractive potential, the other with an equally strong repulsive potential

Separability of the Planar 1/ρ\u3csup\u3e2\u3c/sup\u3e Potential in Multiple Coordinate Systems

With a number of special Hamiltonians, solutions of the Schrödinger equation may be found by separation of variables in more than one coordinate system. The class of potentials involved includes a number of important examples, including the isotropic harmonic oscillator and the Coulomb potential. Multiply separable Hamiltonians exhibit a number of interesting features, including “accidental” degeneracies in their bound state spectra and often classical bound state orbits that always close. We examine another potential, for which the Schrödinger equation is separable in both cylindrical and parabolic coordinates: A z-independent V∝1/ρ2=1/(x2+y2) role= presentation style= box-sizing: border-box; max-height: none; display: inline; line-height: normal; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; min-width: 0px; min-height: 0px; border: 0px; padding: 0px; margin: 0px; position: relative; \u3eV∝1/ρ2=1/(x2+y2) in three dimensions. All the persistent, bound classical orbits in this potential close, because all other orbits with negative energies fall to the center at ρ=0 role= presentation style= box-sizing: border-box; max-height: none; display: inline; line-height: normal; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; min-width: 0px; min-height: 0px; border: 0px; padding: 0px; margin: 0px; position: relative; \u3eρ=0. When separated in parabolic coordinates, the Schrödinger equation splits into three individual equations, two of which are equivalent to the radial equation in a Coulomb potential—one equation with an attractive potential, the other with an equally strong repulsive potential

Additional file 1: of Maternal ‘near miss’ collection at an Australian tertiary maternity hospital

King Edward Memorial Hospital Maternal ‘Near Miss’ collection form. Data collection tool for the collection of maternal near miss cases at KEMH. (DOCX 19 kb)