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 back...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.展开更多
This paper describes an easy and teaching way how quantum mechanics (QM) and general relativity (GR) can be brought together. The method consists of formulating Schrödinger’s equation of a free quantum wave of a...This paper describes an easy and teaching way how quantum mechanics (QM) and general relativity (GR) can be brought together. The method consists of formulating Schrödinger’s equation of a free quantum wave of a massive particle in curved space-time of GR using the Schwarzschild metric. The result is a Schrödinger equation of the particle which is automatically subjected to Newtons’s gravitational potential.展开更多
文摘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.
文摘This paper describes an easy and teaching way how quantum mechanics (QM) and general relativity (GR) can be brought together. The method consists of formulating Schrödinger’s equation of a free quantum wave of a massive particle in curved space-time of GR using the Schwarzschild metric. The result is a Schrödinger equation of the particle which is automatically subjected to Newtons’s gravitational potential.
