A Note on Wigner Functions and *-Genvalue Equation

作者：Jing Si Cong^*; Lin Bing Sheng

来源：Communications in Theoretical Physics, 2009, 51(4): 605-608.

DOI：10.1088/0253-6102/51/4/06

• Wigner function
• *-genvalue equation
• deformation quantization

In deformation quantization, static Wigner functions obey functional *-genvalue equation, which is equivalent to time-independent Schrodinger equation in Hilbert space operator formalism of quantum mechanics. This equivalence is proved mostly for Hamiltonian with form (H) over cap = (1/2) (p) over cap (2) V (<((x))over cap>) [D. Fairlie, Proc. Camb. Phil. Soc. 60 (1964) 581]. In this note we generalize this proof to a very general Hamiltonian (H) over cap ((x) over cap, (p) over cap) and give examples to support it.

• 出版日期2009-4
• 单位中国科学技术大学