Relativistic Schrodinger Wave Equation for Hydrogen Atom Using Factorization Method

In this investigation a simple method developed by introducing spin to Schrodinger equation to study the relativistic hydrogen atom. By separating Schrodinger equation to radial and angular parts, we modify these parts to the associated Laguerre and Jacobi differential equations, respectively. Bound state Energy levels and wave functions of relativistic Schrodinger equation for Hydrogen atom have been obtained. Calculated results well matched to the results of Dirac’s relativistic theory. Finally the factorization method and supersymmetry approaches in quantum mechanics, give us some first order raising and lowering operators, which help us to obtain all quantum states and energy levels for different values of the quantum numbers n and m.

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.

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.

Confined State and Electronic Transport in an Artificial Graphene-Based Tunnel Junction

Artificial graphene structures embedded in semiconductors could open novel routes for studies of electron interactions in 1ow-dimensional systems. We propose a way to manipulate the transport properties of massless Dirac fermions in an artificial graphene-based tunnel junction. Velocity-modulation control of electron wave propagation in the different regions can be regarded as velocity barriers. Transmission probability of electron is affected profoundly by this velocity barrier. We find that there is no confinement for Dirac electron as the velocity ratio ζ is less than 1, but when the velocity ratio is larger than 1 the confined state appears in the continuum band. These localized Dirac electrons may lead to the decreasing of transmission probability.

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.

Quantum Mechanics and Special Relativity:The Origin of Momentum Operator

The free relativistic particle, by definition, has to move in an inertial reference frame with uniform velocity less than the speed of light. The corresponding movement of a material quantum particle describes a wave packet, composed of matter waves—solutions of the Schr?dinger equation. The maximum of packet, corresponding to the largest probability to find the particle, has to move with the same uniform velocity, defined by the initial condition. It has been shown that the traditional definition of the quantum momentum operator i.e. taking it to correspond to the special relativity theory, relativistic momentum, cannot produce precise description of a relativistic matter particle. Different definitions are investigated and one that solves this issue is found. Obtained original expression of relativistic kinetic energy operator creates new possibilities for relativistic quantum systems theory.

Relativistic Landau quantization in the spiral dislocation spacetime

We analyse the interaction of a relativistic electron with a uniform magnetic field in the spiral dislocation spacetime.We show that analytical solutions to the Dirac equation can be obtained,where the spectrum of energy corresponds to the relativistic Landau levels.We also analyse the influence of the spiral dislocation on the relativistic Landau levels by showing that there exists an analogue of the Aharonov–Bohm effect for bound states.

Klein–Gordon oscillator with magnetic and quantum flux fields in non-trivial topological space-time

The relativistic quantum motions of the oscillator field(via the Klein–Gordon oscillator equation)under a uniform magnetic field in a topologically non-trivial space-time geometry are analyzed.We solve the Klein–Gordon oscillator equation using the Nikiforov-Uvarov method and obtain the energy profile and the wave function.We discuss the effects of the non-trivial topology and the magnetic field on the energy eigenvalues.We find that the energy eigenvalues depend on the quantum flux field that shows an analogue of the Aharonov–Bohm effect.Furthermore,we obtain the persistent currents,the magnetization,and the magnetic susceptibility at zero temperature in the quantum system defined in a state and show that these magnetic parameters are modified by various factors.

Aharonov-Bohm effect for bound states on spin-0 massive charged particles in a Gödel-type space-time with Coulomb potential

In this paper,we investigate the relativistic quantum dynamics of spin-0 massive charged particles in a G?del-type space-time with electromagnetic interactions.We derive the radial wave equation of the Klein-Gordon equation with an internal magnetic flux field and Coulombtype potential in the Som-Raychaudhuri space-time with cosmic string.We solve this equation and analyze the analog effect in relation to the Aharonov-Bohm effect for bound states.

Electron-Positron Pair Production in Strong Fields Characterized by Conversion Energy

It is demonstrated that the production mechanism of a pair which is produced from vacuum under an external field can be characterized by its conversion energy, a quantity defined as total mass-energy of this pair. The value of this quantity is checked with quantum field theoretical simulations for several field configurations and it is found that conversion energy can show all the production channels and give the yields of each channel specifically. We detect signatures of effective mass, combination of different photons as well as dynamically assisted Schwinger mechanism and represented more features of these processes in the view of conversion energy.