关键词: 狄拉克振子, 非对易相空间, Wigner 函数, 能级

Abstract: With the development of noncommutative geometry，string theory and loop quantum gravity theory，he noncommutative space has been made more and more concerned. The noncommutative quantum theory is different from the ordinary quantum theory，which is a special physical effect under the string scale. Therefore，special methods are needed to deal with noncommutative quantum mechanics problems. In this paper，the Moyal equationand Wigner function first are introduced. Starting from Moyal-Weyl multiplication and Bopp transformation，H(x，p)is transformed into H^ (x^ ，p^ )by considering the noncommutability of coordinate-coordinate，momentum-momen tum to realize the star-multiplication eigenequation in the non-commutative phase space. The algebraic relationship of noncommutative phase space quantum mechanics is used to discuss the Wigner functions and energy levels of Dirac oscillator in noncommutative phase space. The results show that the energy level of the Dirac oscillator in the non-commutative phase space is obviously dependent on non-commutative parameters.

Key words: Dirac oscillator, noncommutative phase space, wigner function, energy