106 research outputs found

    Planar Dirac Electron in Coulomb and Magnetic Fields: a Bethe ansatz approach

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    The Dirac equation for an electron in two spatial dimensions in the Coulomb and homogeneous magnetic fields is an example of the so-called quasi-exactly solvable models. The solvable parts of its spectrum was previously solved from the recursion relations. In this work we present a purely algebraic solution based on the Bethe ansatz equations. It is realised that, unlike the corresponding problems in the Schr\"odinger and the Klein-Gordon case, here the unknown parameters to be solved for in the Bethe ansatz equations include not only the roots of wave function assumed, but also a parameter from the relevant operator. We also show that the quasi-exactly solvable differential equation does not belong to the classes based on the algebra sl2sl_2.Comment: LaTex, 12 pages, no figure

    The effect of a smartphone-based coronary heart disease prevention (SBCHDP) programme on awareness and knowledge of CHD, stress, and cardiac-related lifestyle behaviours among the working population in Singapore: a pilot randomised controlled trial

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    Background: Coronary heart disease (CHD) is the most prevalent type of cardiac disease among adults worldwide, including those in Singapore. Most of its risk factors, such as smoking, physical inactivity and high blood pressure, are preventable. mHealth has improved in the last decade, showing promising results in chronic disease prevention and health promotion worldwide. Our aim was to develop and examine the effect of a 4-week Smartphone-Based Coronary Heart Disease Prevention (SBCHDP) programme in improving awareness and knowledge of CHD, perceived stress as well as cardiac-related lifestyle behaviours in the working population of Singapore. Methods: The smartphone app “Care4Heart” was developed as the main component of the programme. App content was reviewed and validated by a panel of experts, including two cardiologists and two experienced cardiology-trained nurses. A pilot randomised controlled trial was conducted. Eighty working people were recruited and randomised to either the intervention group (n = 40) or the control group (n = 40). The intervention group underwent a 4-week SBCHDP programme, whereas the control group were offered health promotion websites only. The participants’ CHD knowledge, perceived stress and behavioural risk factors were measured at baseline and on the 4th week using the Heart Disease Fact Questionnaire-2, Perceived Stress Scale, and Behavioural Risk Factor Surveillance System. Results: After the SBCHDP programme, participants in the intervention group had a better awareness of CHD being the second leading cause of death in Singapore (X 2  = 6.486, p = 0.039), a better overall CHD knowledge level (t = 3.171, p = 0.002), and better behaviour concerning blood cholesterol control (X 2 = 4.54, p = 0.033) than participants in the control group. Conclusion: This pilot study partially confirmed the positive effects of the SBCHDP programme in improving awareness and knowledge of CHD among the working population. Due to the small sample size and short follow-up period, this study was underpowered to detect significant differences between groups. A full-scale longitudinal study is required in the future to confirm the effectiveness of the SBCHDP programme

    Charged particles in external fields as physical examples of quasi-exactly solvable models: a unified treatment

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    We present a unified treatment of three cases of quasi-exactly solvable problems, namely, charged particle moving in Coulomb and magnetic fields, for both the Schr\"odinger and the Klein-Gordon case, and the relative motion of two charged particles in an external oscillator potential. We show that all these cases are reducible to the same basic equation, which is quasi-exactly solvable owing to the existence of a hidden sl2sl_2 algebraic structure. A systematic and unified algebraic solution to the basic equation using the method of factorization is given. Analytic expressions of the energies and the allowed frequencies for the three cases are given in terms of the roots of one and the same set of Bethe ansatz equations.Comment: RevTex, 15 pages, no figure

    Quasi-exact solvability of Dirac equation with Lorentz scalar potential

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    We consider exact/quasi-exact solvability of Dirac equation with a Lorentz scalar potential based on factorizability of the equation. Exactly solvable and sl(2)sl(2)-based quasi-exactly solvable potentials are discussed separately in Cartesian coordinates for a pure Lorentz potential depending only on one spatial dimension, and in spherical coordinates in the presence of a Dirac monopole.Comment: 10 pages, no figure
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