Winger Function for Spin Half Non-commutative Landau Problem

Key words: 
• spin half Landau problem /
• Wigner function /
• noncommutative phase space /
• uniform magnetic field

Abstract: With great significance in describing the state of quantum system, the Wigner function of the spin half noncommutative Landau problem is studied in this paper. On the basis of the review of the Wigner function in the commutative space, which is subject to the *eigenvalue equation, Hamiltonian of the spin half Landau problem in the noncommutative phase space is given. Then, energy levels and Wigner functions in the form of a matrix of the spin half Landau problem in the noncommutative phase space are obtained by means of the _^*-eigenvalue equation (or Moyal equation).