| Relativity and quantum theory are the two cornerstones of modern physics,their successive establishment has brought profound changes in people’s understanding about the whole theoretical basis of physics.It is well known that quantum field theory,based on special relativity and quantum theory,has achieved remarkable achievements,especially for the unified description of strong,weak and electromagnetic interactions.However,with the continuous development of research,physicists found that in the face of some extreme phenomena such as the description of the big bang and black hole singularity,the object mass is very large while the scale is very small,if you use one of the theories of relativity and quantum theory to describe it,it can not be explained and predicted appropriately.As a result,researchers began to unify relativity and quantum theory,which is exactly what many physicists have been working on.However,due to the highly nonlinear nature of Einstein’s gravitational field equation,there are great difficulties in quantization of gravity,which makes it difficult to reconcile the contradiction between quantum theory and general relativity.Therefore,the researchers made many attempts to unify quantum theory and general relativity,and one kind of attempt is the superstring theory,the second one is incorporating the influnces of gravity to quantum theories by modifying the basic commutators among canonical variables,noncommutativity and the generalized uncertainty principle(GUP)can be regarded as examples of such attempt.In order to deepen our knowledge of the noncommutative formalism and GUP to explore the influence of noncommutative effect and the gravitational effect on traditional physical system,this work focuses on the following aspects:(1)we study the anharmonic oscillator for unrelativistic and relativistic(K-G equation)cases in noncommutative plane.By employing Bopp shift and the functional analysis method,the energy eigenvalues and corresponding wave function of Schr?dinger equation in the presence of the anharmonic oscillator under an external magnetic field in noncommutative plane and K-G equation in the presence of the anharmonic oscillator under an external magnetic field in noncommutative plane are obtained,they show that the noncommutative parameter shifts the energy levels of the system.Subsequently,we theoretically deduce the effective Boltzmann factor of the q-deformed superstatistics,and expressed the partition function and the thermodynamic function of the corresponding system.In order to make these functions clear to discuss,we depict some figures to analysize them.It shows that for the case of Schr?dinger equation in the presence of the anharmonic oscillator under an external magnetic field in noncommutative plane,the effect of the NC parameter on the quantities is significant,especially for the Helmholtz free energy and the specific heat.And for another case,it shows that the symmetric and unsymmetric formalism of the scalar potential and vector potential for K-G equation,the changing trends of the curves on the partition function and the thermodynamical properties ensemble are analogous,and the effect of the NC parameter on the system considered is significant.(2)We study the solutions of the Schr?dinger equation under topological defects space-times and generalized uncertainty principle.By using the Bethe ansatz method,the energy eigenvalues and corresponding wave function are obtained,it shows that the GUP parameter shifts the energy levels of the system.Through the analysis of the system,considering the deviation on the standard quantum mechanics because of the influence of the gravity,we derive the magnitude of the GUP parameter by comparison with the experimental result.And for the study of Kemmer oscillator under GUP,by employing the functional analysis method,the energy eigenvalues,the wave function and the corresponding probability density of every component are obtained.In order to facilitate the analysis,we depict some figures to discuss the effects of the GUP parameter on the energy spectrum and the thermodynamic property of the system.It shows that for the same principal quantum number,the energy increases monotonically with the increase of the GUP parameter,and for the thermodynamic properties of the system,the effect of gravity shifts the partition function,the free energy,the mean energy,the specific heat and the entropy,especially for the high temperature limit,the effect of the GUP parameter on specific heat is observable.(3)We study the(2+1)-Dimensional DKP Oscillator(spin-0 and spin-1)under a magnetic field in the presence of a minimal length in the noncommutative Space.By employing the Bopp shift and the functional analysis method,the energy eigenvalues,the wave function and the corresponding probability density of every component are obtained,and on this basis we depict a figure to show the variation curve of the energy spectrum.Due to the complexity of the expression of energy spectrum,we discuss it in two cases,i.e.the spin-0 and the spin-1.It shows that for the case of spin-0,the energy eigenvalues increase monotonically with the magnetic field variable B for the minimal length parameter and the NC parameter,respectively,and for one principal quantum number,the energy increases with the increase of the azimuthal quantum number.Regard to the case of spin-1,it shows that for the same azimuthal quantum number,the energy increases monotonically with the increase of the noncommutative parameter and GUP parameter.In addition,we discuss the special cases of the energy for spin-0 and spin-1,their results have an analogous variation tendency. |
