Solution of the Hamilton – Jacobi Equation in a Central Potential Using the Separation of Variables Method with Staeckel Boundary Conditions

This manuscript aims at solving Hamilton-Jacobi equation in a central potential using the separation of variables technique with Staeckel boundary conditions. Our results show that the Hamilton – Jacobi variables can be completely separated, which agrees with other results employing different methods. Keywords: Lagrangian mechanics, Hamilton-Jacobi, Staeckel boundary conditions, Staeckel matrix, Staeckel vector, Hamilton's characteristic function, Hamilton's principal function.

The HVT Technique and the "Uncertainty" Relation for Central

The quantum mechanical hypervirial theorems (HVT) technique is used to treat the so-called "uncertainty" relation for quite a wide class of central potential wells, including the (reduced) Poeschl-Teller and the Gaussian one.It is shown that this technique is quite suitable in deriving an approximate analytic expression in the form of a truncated power series expansion for the dimensionless product $P_{nl}\equiv <r^2>_{nl}<p^2>_{nl}/\hbar^2$, for every (deeply) bound state of a particle moving non-relativistically in the well, provided that a (dimensionless) parameter s is sufficiently small. Numerical results are also given and discussed.

An introduction to analysis of R\’enyi complexity ratio of quantum states for central potential

R\’enyi complexity ratio of two density functions is introduced for three and multidimensional quantum systems. Localization property of several density functions are defined and five theorems about near continuous property of R\’enyi complexity ratio are proved by Lebesgue measure. Some properties of R\’enyi complexity ratio are demonstrated and investigated for different quantum systems. Exact analytical forms of R\’enyi entropy, R\’enyi complexity ratio, statistical complexities based on R\’enyi entropy for integral order have been presented for solutions of pseudoharmonic and a family of isospectral potentials. Some properties of R\’enyi complexity ratio are verified for six diatomic molecules (CO, NO, N$_2$, CH, H$_2$, and ScH) and for other quantum systems.

Effects of Linear Central Potential Induced by Lorentz Symmetry Violation framework and Cornell-type Non-electromagnetic Potential on Spin-0 Scalar Particles

The relativistic quantum dynamics of a spin-0 scalar particle under the effects of the violation of Lorentz symmetry in the presence of a non-electromagnetic potential is analyzed. The central potential induced by the Lorentz symmetry violation is a linear electric and constant magnetic field and, analyze the effects on the eigenvalues and the wave function. We see there is a dependence of the linear charge density on the quantum numbers of the system

Linear Central Potential Effects Induced by Lorentz Symmetry Violation on Spin-0 Particle Under Coulomb-type scalar Potential

In this work, quantum dynamics of a spin-0 particle under the effects of Lorentz symmetry violation in the presence of Coulombtype non-electromagnetic potential $(S(r) &prop; \frac{1}{r})$ is investigated. The non-electromagnetic (or scalar) potential is introduced by modifying the mass term via transformation $M &rarr; M + \frac{&eta;_c}{r}$ in the relativistic wave equation. The linear central potential induced by the Lorentz symmetry violation is a linear radial electric and constant magnetic field and, analyze the effects on the spectrum of energy and the wave function

Particle Theory: A New Theory That May Reconcile General Relativity and Quantum Theory

In an attempt to reconcile General Relativity and Quantum Mechanics, Particle Theory is a concept that may try to address this issue. This theory explains the effects accurately calculated by General Relativity in an alternate and real, physical way, and is therefore an alternative to GR. The theory states that indivisible atomic particles are instead divided into even smaller particles (called “EM particles”) held together by a central potential, the speed of light being the limit to their velocities. The “shedding” of these particles are responsible for the static and magnetic fields we observe. This also creates a “screening” effect that, for an atomic particle at rest, blocks about half of what this theory defines as the “true gravitational potential”, which is just twice the Newtonian value (mediated by what this theory defines as “gravity particles”). When an atomic system of particles starts moving in a certain direction, the act of shedding and the internal movement decreases as the particles orient themselves in the direction of the velocity, which reduces the screening effect, where we start to observe the relativistic effects of General (and Special) Relativity.