Scalar potential

About: Scalar potential is a research topic. Over the lifetime, 3642 publications have been published within this topic receiving 78868 citations. The topic is also known as: potential.

The Galilean covariance of quantum mechanics in the case of external fields

Abstract: Textbook treatments of the Galilean covariance of the time-dependent Schrodinger equation for a spinless particle seem invariably to cover the case of a free particle or one in the presence of a scalar potential. The principal objective of this paper is to examine the situation in the case of arbitrary forces, including the velocity-dependent variety resulting from a vector potential. To this end, we revisit the 1964 theorem of Jauch which purports to determine the most general form of the Hamiltonian consistent with “Galilean-invariance,” and argue that the proof is less than compelling. We then show systematically that the Schrodinger equation in the case of a Jauch-type Hamiltonian is Galilean covariant, so long as the vector and scalar potentials transform in a certain way. These transformations, which to our knowledge have appeared very rarely in the literature on quantum mechanics, correspond in the case of electrodynamical forces to the “magnetic” nonrelativistic limit of Maxwell’s equations in the...

Discussion about the analytical calculation of the magnetic field created by permanent magnets

Abstract: This paper presents an improvement of the calculation of the magnetic field components created by ring permanent magnets. The three-dimensional approach taken is based on the Coulombian Model. Moreover, the magnetic field components are calculated without using the vector potential or the scalar potential. It is noted that all the expressions given in this paper take into account the magnetic pole volume density for ring permanent magnets radially magnetized. We show that this volume density must be taken into account for calculating precisely the magnetic field components in the near-field or the far-field. Then, this paper presents the component switch theorem that can be used between infinite parallelepiped magnets whose cross-section is a square. This theorem implies that the magnetic field components created by an infinite parallelepiped magnet can be deducted from the ones created by the same parallelepiped magnet with a perpendicular magnetization. Then, we discuss the validity of this theorem for axisymmetric problems (ring permanent magnets). Indeed, axisymmetric problems dealing with ring permanent magnets are often treated with a 2D approach. The results presented in this paper clearly show that the two-dimensional studies dealing with the optimization of ring permanent magnet dimensions cannot be treated with the same precisions as 3D studies.

Consequences of particle conservation along a flux surface for magnetotail tearing

Abstract: The energy principle for magnetotail tearing is reexamined using conservation of electron particle number along a flux surface as a means of calculating the volume-integrated perturbed number density 〈 n1 〉, where n1 is the perturbed electron number density and the angle brackets denote integration along a field line. It is shown that if the electron response is magnetohydrodynamic, then 〈 n1 〉 can be calculated as a function of the perturbation vector potential component A1y (assuming magnetotail coordinates) independent of the potential components A1x and A1z and independent of the scalar potential ϕ. This result holds as long as the equilibrium and the tearing perturbations are two-dimensional, independent of the y coordinate. In the case of a parabolic field model, the resulting 〈 n1 〉 exactly matches the results obtained previously by Lembege and Pellat [1982], who used the kinetic drift equation to calculate the electron response. Thus the compressional stabilization of the tearing mode is a direct consequence of, and can be completely calculated from, the conservation of electron particle number along the field line. Further, it is shown that 〈 n1 〉 is independent of By, the guide component of the magnetic field, so the inclusion of a guide field does not alter the tearing stabilization condition.

An H-formulation-based three-dimensional hysteresis loss modelling tool in a simulation including time varying applied field and transport current: the fundamental problem and its solution

Abstract: When analytic solutions are not available, finite-element-based tools can be used to simulate hysteresis losses in superconductors with various shapes. A widely used tool for the corresponding magnetoquasistatic problem is based on the H-formulation, where H is the magnetic field intensity, eddy current model. In this paper, we study this type of tool in a three-dimensional simulation problem. We consider a case where we simultaneously apply both a time-varying external magnetic field and a transport current to a twisted wire. We show how the modelling decisions (air has high finite resistivity and applied field determines the boundary condition) affect the current density distribution along the wire. According to the results, the wire carries the imposed net current only on the boundary of the modelling domain, but not inside it. The current diffuses to the air and back to the boundary. To fix this problem, we present another formulation where air is treated as a region with 0 conductivity. Correspondingly, we express H in the air with a scalar potential and a cohomology basis function which considers the net current condition. As shown in this paper, this formulation does not fail in these so-called AC-AC (time varying transport current and applied magnetic field) simulations.

Scalar field, nonminimal coupling, and cosmology.

Abstract: We study the dynamics of a flat Friedmann-Robertson-Walker universe filled with a self-interacting scalar field nonminimally coupled to the gravitational field. Dynamical equations for the system can be derived from a pointlike Lagrangian. For this system an additional Noether symmetry exists provided that the coupling constant {xi} is equal to 0 or 1/6. When {xi}=1/6 the scalar potential has to be constant. In this case we obtain an exact solution. We also analyze the behavior of the scalar field when {xi}{ne}0, 1/6. Most of the considered solutions are unphysical but there exists a very interesting case in which the effective cosmological constant is rapidly changing, which might lead to inflation.