The Study Of The Quantum Harmonic Oscillator In Noncommutative Space

In order to explore the influence of noncommutative effect on traditional physical systems,we study the(2+1)dimensional Kemmer oscillator in noncommutative space and express the energy eigenvalue and the wave function of the system.Subsequently,motivated by this work,we study the(2+1)-dimensional Klein–Gordon oscillator under a magnetic field in the presence of a minimal length in the noncommutative space.The article will proceed from the following aspects.1: We study the(2+1)dimensional Kemmer oscillator in noncommutative space.The noncommutative system is transformed into the commutative system via the coordinate space representation,the energy eigenvalue and the wave function of the system are obtained by the confluent hypergeometric function.The result show that the noncommutative effect will change the energy eigenvalue and the wave function of the system.2: The(2 +1)-dimensional Klein–Gordon oscillator under a magnetic field in the presence of a minimal length in the NC space is solved in the momentum space.We first analyze the Klein–Gordon oscillator in the presence of a minimal length in NC space,and obtain the energy spectrum as well as the wave functions in terms of the Jacobi polynomials.Subsequently,we generalize this quantum model into the framework of a magnetic field and express the corresponding results,respectively.Finally,by depicting the numerical results via the Mathematica,we compare our result with the previous one and discuss the corresponding special cases.It shows that the energy eigenvalues increase monotonically with the magnetic field variable for the minimal length parameter and the NC space parameter,respectively,and for one principal quantum number,the energy increases with the increase of the azimuthal quantum number.