Title: Quantization of a one-dimensional system by means of the quantum Hamilton-Jacobi equation Author:Girard, Mario Fusco Subject:Quantum Physics Description:
The numerical version of the Hamilton-Jacobi quantization method, recently proposed, is applied to the one dimensional quartic oscillator. A suitable quantization condition is formulated and various energy levels and wave functions are computed. The results very well agree with those obtained by means of the Schroedinger equation, and confirm that the Quantum Hamilton Jacobi approach, which is the exact version of the semiclassical WKB scheme, is a self-contained quantization procedure, equivalent and independent from the Schoedinger's one but more general. Indeed, with respect to this latter, the Quantum Hamilton-Jacobi equation can be used to investigate the limit h->0, where the Schroedinger equation loses its significance, and explains how the fundamental quantities of the classical mechanics, the Hamilton's characteristic function and the classical momentum, are generated from the corresponding quantum ones.
1711.09552 (ARXIV ID)
Title: Numerical solutions of the quantum Hamilton-Jacobi equation and WKB like representations for one dimensional wave functions Author:Girard, Mario Fusco Subject:Quantum Physics Description:
By means of numerical solutions of the quantum Hamilton Jacobi equation, a general WKB-like representation for one-dimensional wave functions is obtained. This representation is unique in the classically forbidden regions, while in the allowed one, each wave function corresponds to a one parameter family of solutions of the QHJE. The method has been applied to various systems, with different energies and initial conditions. In all investigated cases, the wave functions so obtained accurately reproduce the solutions of the Schr\"odinger equation, analytically or numerically computed by other ways. Some results for harmonic oscillator and radial Coulomb motion are presented. Comment: 6 pages, 4 figures
1403.0825 (ARXIV ID)
Title: Analytical Solutions of the Quantum Hamilton-Jacobi Equation and Exact WKB-Like Representations of One-Dimensional Wave Functions Author:Girard, Mario Fusco Subject:Quantum Physics Description:
General analytical solutions of the Quantum Hamilton Jacobi Equation for conservative one-dimensional or reducible motion are presented and discussed. The quantum Hamilton's characteristic function and its derivative, i.e. the quantum momentum function, are obtained in general, and it is shown that any one-dimensional wave function can be exactly represented in a WKB-like form. The formalism is applied to the harmonic oscillator and to the electron's motion in the hydrogen atom, and the above mentioned functions are computed and discussed for different quantum numbers. It is analyzed how the quantum quantities investigated tend to the corresponding classical ones, in the limit $\hbar\to 0$. These results demonstrate that the Quantum Hamilton Jacobi Equation is not only completely equivalent to the Schr\"odinger Equation, but allows also to fully investigate the transition from quantum to classical mechanics.
1512.01356 (ARXIV ID)
Title: Comment on ' Computational method for the quantum Hamilton-Jacobi equation: Bound states in one dimension' [J. Chem. Phys. 125, 174103 (2006)] Author:Girard, Mario Fusco Subject:Quantum Physics ; 81sxx Description:
Some difficulties, both numerical and conceptual, of the method to compute one dimensional wave functions by numerically integrating the quantum Hamilton-Jacobi equation, presented in the paper mentioned in the title, are analyzed. The origin of these difficulties is discussed, and it is shown how they can be avoided by means of another approach, based on different solutions of the same equation. Results for the same potentials, obtained by this latter method are presented and a comparison is made. Comment: 4 figures
1404.0858 (ARXIV ID)
Title: Reliability of First-Trimester Ultrasonic Biopsy for the Evaluation of Placental and Myometrial Blood Perfusion and the Prediction of Preeclampsia Author:Markey, Stephanie; Demers, Suzanne; Girard, Mario; Tétu, Amélie; Gouin, Katy; Bujold, Emmanuel Subject:Pregnancy ; Doppler ; Placenta ; Preeclampsia ; Three-Dimensional ; Ultrasound ; Imaging, Three-Dimensional ; Myometrium ; Placenta ; Pre-Eclampsia ; Ultrasonography, Prenatal Description:
Low placental vascularization measured by three-dimensional (3-D) ultrasound with power Doppler can predict preeclampsia. We evaluated the reliability and reproducibility of the ultrasonic sphere biopsy (USSB) technique to evaluate placental and subplacental myometrium vascularization in the first trimester. We performed a secondary analysis of a case-control study nested in a prospective cohort of women with a singleton pregnancy undergoing ultrasound at 11 to 14 weeks' gestation. Women who developed preeclampsia (n = 20) and randomly selected controls (n = 60) were compared. Other controls (n = 60) were also randomly selected to evaluate intra- and inter-observer reproducibility. Using 3-D power Doppler, the vascularization index (VI), flow index (FI), and vascularization flow index (VFI) were measured from the volume of the whole placenta and the subplacental myometrium and from their respective USSB. Pearson's correlation coefficients (cc) with their P-values were calculated. We observed that USSB is reliable in estimating the vascularization of the whole placenta in the first trimester (cc of VI 0.83; of FI 0.62; and of VFI 0.78; P < 0.001 for all) but was not as reliable for estimating subplacental myometrium vascularization (cc of VI 0.71; of FI 0.35; and of VFI 0.73). Measurement of placental vascularization using USSB showed good to excellent intra- and inter-observer reproducibility (cc of VI 0.86 and 0.85, respectively; of FI 0.75 and 0.75, respectively; and of VFI 0.83 and 0.83, respectively; P < 0.001 for all). Finally, we observed that women who subsequently developed preeclampsia had lower placental USSB VI (2.1 vs 4.8, P = 0.02), FI (32.4 vs. 42.5, P = 0.002), and VFI (0.8 vs. 2.1, P = 0.01) than controls. First-trimester USSB of the placenta using 3-D power Doppler is a reliable and reproducible procedure for estimating placental vascularization and could be used to predict preeclampsia.
Is part of:
Journal of obstetrics and gynaecology Canada : JOGC = Journal d'obstetrique et gynecologie du Canada : JOGC, November 2016, Vol.38(11), pp.1003-1008
1701-2163 (ISSN); 27969552 Version (PMID); 10.1016/j.jogc.2016.09.003 (DOI)
Title: Evaluation of fetal liver volume by tridimensional ultrasound in women with gestational diabetes mellitus Author:Dubé, Marie-Christine; Girard, Mario; Morisset, Anne-Sophie; Tchernof, André; Weisnagel, S John; Bujold, Emmanuel Subject:Ultrasonography, Prenatal ; Diabetes, Gestational -- Diagnostic Imaging ; Liver -- Diagnostic Imaging Description:
To evaluate the effect of gestational diabetes mellitus (GDM) on fetal liver growth during the third trimester. We performed a longitudinal study of pregnant women recruited at the time of GDM screening (24 to 28 weeks of gestation), with follow-up visits at 32 weeks, 36 weeks, and delivery. Women with GDM were followed with nutritional recommendations and insulin when necessary according to the Canadian Diabetes Association guidelines. Fetal liver volume was evaluated using 3-D ultrasound at each antenatal visit, and fetal liver growth was compared between women with and without GDM. Twenty-seven women were recruited, 10 with normal glucose tolerance (NGT) and 17 with confirmed GDM, five who required insulin and 12 who were treated by diet only. We found no difference in fetal liver volume between groups at any of the three visits, and median birth weight was also similar between groups. On the other hand, we found a strong correlation between fetal liver volume at 36 weeks' gestation and birth weight (ρ = 0.61, P < 0.001). In our preliminary study, we found that fetal liver volume could be a strong predictor of infant birth weight independent of GDM status. This suggests that fetal liver volume of offspring of women with NGT is similar to that of offspring of women with GDM treated following recommended targets. Larger studies are required.
Is part of:
Journal of obstetrics and gynaecology Canada : JOGC = Journal d'obstetrique et gynecologie du Canada : JOGC, November 2011, Vol.33(11), pp.1095-8
1701-2163 (ISSN); 22082782 Version (PMID)