Relativistic Dynamics of a Quantum System

In this paper, we examine quantum systems with relativistic dynamics. We show that for a successful description of these systems, the application of Galilei invariant nonrelativistic Hamiltonian is necessary. To modify this Hamiltonian to relativistic dynamics, we require precise relativistic kinetic energy operators instead of nonrelativistic ones for every internal (Jacobi) coordinate. Finally, we introduce and investigate the Schr&oumldinger equation with relativistic dynamics for two-particle systems with harmonic oscillator and Coulomb potentials.

Kinematic Relativity of Quantum Mechanics:Free Particle with Different Boundary Conditions

An investigation of origins of the quantum mechanical momentum operator has shown that it corresponds to the nonrelativistic momentum of classical special relativity theory rather than the relativistic one, as has been unconditionally believed in traditional relativistic quantum mechanics until now. Taking this correspondence into account, relativistic momentum and energy operators are defined. Schr&oumldinger equations with relativistic kinematics are introduced and investigated for a free particle and a particle trapped in the deep potential well.

Structure of Schrodinger’s Nucleon.Density Distributions and Zemach Momenta

The recently introduced Galilei invariant model of the nucleon as a system of three point particles, whose dynamics is governed by Schr?dinger equation, is applied for nucleon structure investigation. The obtained charge, magnetism, mass and point particles density distributions of the proton and neutron are in satisfactory agreement with known information about nucleon structure. The model predicts the third Zemach momentum of proton larger than the one obtained in dipole approximation and larger than following from electron-proton data analysis.

Structure of Schrodinger’s Nucleon:Elastic Form-Factors and Radii

The Galilei invariant model of the nucleon as a system of three point particles, whose dynamics is governed by Schr?dinger equation, after six Hamiltonian parameters fitting, predicts magnetic momenta, masses and charge radii of the proton and neutron with experimental precision. Now this model is applied in order to investigate nucleon charge, mass and magnetism distributions. The obtained electric and magnetic form factors at low values of momentum transfer are in satisfactory agreement with experimental information. The model predicts that neutron is a more compact system than proton.

Ground State Nucleon, Dark Energy and Dark Matter

The recently introduced model of the nucleon as a system of three point particles predicts all characteristics of the proton and neutron with experimental precision only at condition that nucleon is the loosely bound state in system of deep potential wells. The model’s Hamiltonian contains ground state with the same parity and spin as the nucleon but with other different characteristics. Existence of this ground state nucleon means that the visible Universe is composed of excited matter. The direct transition between excited and ground states is strictly forbidden, however, stimulated emission can ignite such process. Most likely, corresponding conditions realize at supernova explosion. It is shown that presence of this matter, composed of ground state nucleons, in Universe gives the chance for consistent explanation of dark matter and dark energy phenomena.

Study of scalar particles through the Klein–Gordon equation under rainbow gravity effects in Bonnor–Melvin-Lambda space-time

In our investigation,we explore the quantum dynamics of charge-free scalar particles through the Klein–Gordon equation within the framework of rainbow gravity,considering the Bonnor–Melvin-Lambda(BML)space-time background.The BML solution is characterized by the magnetic field strength along the axis of the symmetry direction which is related to the cosmological constantΛand the topological parameterαof the geometry.The behavior of charge-free scalar particles described by the Klein–Gordon equation is investigated,utilizing two sets of rainbow functions:(i)f(χ)=■,h(χ)=1 and(ii)f(χ)=1,h(χ)=1+βХ/2.Here 0<(Х=■)≤1 with E representing the particle's energy,Ep is the Planck's energy,andβis the rainbow parameter.We obtain the approximate analytical solutions for the scalar particles and conduct a thorough analysis of the obtained results.Afterwards,we study the quantum dynamics of quantum oscillator fields within this BML space-time,employing the Klein–Gordon oscillator.Here also,we choose the same sets of rainbow functions and obtain the approximate eigenvalue solution for the oscillator fields.Notably,we demonstrate that the relativistic approximate energy profiles of charge-free scalar particles and oscillator fields get influenced by the topology of the geometry and the cosmological constant.Furthermore,we show that the energy profiles of scalar particles receive modifications from the rainbow parameter and the quantum oscillator fields by both the rainbow parameter and the frequency of oscillation.

Topological effects on non-relativistic eigenvalue solutions under AB-flux field with pseudoharmonic- and Mie-type potentials

In this paper,we investigate the quantum dynamics of a non-relativistic particle confined by the Aharonov-Bohm quantum flux field with pseudoharmonic-type potential in the background of topological defect produced by a point-like global monopole.We solve the radial Schrödinger equation analytically and determine the exact eigenvalue solution of the quantum system.Afterwards,we consider a Mie-type potential in the quantum system and solve the radial equation analytically and obtain the eigenvalue solution.We analyze the effects of the topological defect and the quantum flux with these potentials on the energy eigenvalue and wave function of the nonrelativistic particles.In fact,it is shown that the energy levels and wave functions are influenced by the topological defect shifted the result compared to the flat space results.In addition,the quantum flux field also shifted the eigenvalue solutions and an analogue of the Aharonov-Bohm effect for bound-states is observed.Finally,we utilize these eigenvalue solutions to some known diatomic molecular potential models and presented the energy eigenvalue and wave function.