We investigate mass ladder operators for the static BTZ-like black hole in Einstein-bumblebee gravity and probe the quasinormal frequencies of the mapped modes using mass ladder operators for a scalar perturbation und...We investigate mass ladder operators for the static BTZ-like black hole in Einstein-bumblebee gravity and probe the quasinormal frequencies of the mapped modes using mass ladder operators for a scalar perturbation under Dirichlet and Neumann boundary conditions.We find that the mass ladder operators depend on the Lorentz symmetry breaking parameter,and the imaginary parts of the frequencies shifted by the mass ladder operators increase with the increase in the Lorentz symmetry breaking parameter under the two boundary conditions.Note that,under the Neumann boundary condition,the mapped modes caused by the mass ladder operator D_(0,k_(+))are unstable.Moreover,the mass ladder operators do not change the Breitenlohner-Freedman bound for the scalar modes,as in the case of the usual BTZ black hole.These results could aid us in further understanding the conformal symmetry and Lorentz symmetry breaking in Einstein-bumblebee gravity.展开更多
Using ladder operators for the non-linear oscillator with position-dependent effective mass, realization of the dynamic group SU(1,1) is presented. Keeping in view the algebraic structure of the non-linear oscillator,...Using ladder operators for the non-linear oscillator with position-dependent effective mass, realization of the dynamic group SU(1,1) is presented. Keeping in view the algebraic structure of the non-linear oscillator, coherent states are constructed using Barut–Girardello formalism and their basic properties are discussed. Furthermore, the statistical properties of these states are investigated by means of Mandel parameter and second order correlation function. Moreover,it is shown that in the harmonic limit, all the results obtained for the non-linear oscillator with spatially varying mass reduce to corresponding results of the linear oscillator with constant mass.展开更多
A generalized scheme for the construction of coherent states in the context of position-dependent effective mass systems has been presented. This formalism is based on the ladder operators and associated algebra of th...A generalized scheme for the construction of coherent states in the context of position-dependent effective mass systems has been presented. This formalism is based on the ladder operators and associated algebra of the system which are obtained using the concepts of supersymmetric quantum mechanics and the property of shape invariance. In order to exemplify the general results and to analyze the properties of the coherent states, several examples have been considered.展开更多
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 part...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.展开更多
基金Supported by the National Key Research and Development Program of China(2020YFC2201400)the National Natural Science Foundation of China(12275078,12275079,12035005)+1 种基金Hunan Province College Students Research Learning and Innovative Experiment Project(S202210542197)the Innovative Research Group of Hunan Province,China(2024JJ1006)。
文摘We investigate mass ladder operators for the static BTZ-like black hole in Einstein-bumblebee gravity and probe the quasinormal frequencies of the mapped modes using mass ladder operators for a scalar perturbation under Dirichlet and Neumann boundary conditions.We find that the mass ladder operators depend on the Lorentz symmetry breaking parameter,and the imaginary parts of the frequencies shifted by the mass ladder operators increase with the increase in the Lorentz symmetry breaking parameter under the two boundary conditions.Note that,under the Neumann boundary condition,the mapped modes caused by the mass ladder operator D_(0,k_(+))are unstable.Moreover,the mass ladder operators do not change the Breitenlohner-Freedman bound for the scalar modes,as in the case of the usual BTZ black hole.These results could aid us in further understanding the conformal symmetry and Lorentz symmetry breaking in Einstein-bumblebee gravity.
文摘Using ladder operators for the non-linear oscillator with position-dependent effective mass, realization of the dynamic group SU(1,1) is presented. Keeping in view the algebraic structure of the non-linear oscillator, coherent states are constructed using Barut–Girardello formalism and their basic properties are discussed. Furthermore, the statistical properties of these states are investigated by means of Mandel parameter and second order correlation function. Moreover,it is shown that in the harmonic limit, all the results obtained for the non-linear oscillator with spatially varying mass reduce to corresponding results of the linear oscillator with constant mass.
文摘A generalized scheme for the construction of coherent states in the context of position-dependent effective mass systems has been presented. This formalism is based on the ladder operators and associated algebra of the system which are obtained using the concepts of supersymmetric quantum mechanics and the property of shape invariance. In order to exemplify the general results and to analyze the properties of the coherent states, several examples have been considered.
文摘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.
