三维谐振子Wigner函数的星乘解
Solution of Wigner Function’s Star product for 3-D Harmonic Oscillator
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摘要: Wigner函数作为相空间中的一个准概率分布函数， 也是密度矩阵的特殊表示形式， 具有十分重要的物理意义。 首先介绍了Wigner函数的性质及其计算方法， 然后利用星本征方程（Moyal 方程）计算了三维谐振子的Wigner函数。 最后讨论了在相空间中描述声子与电子（或光子）相互作用的方法， 并得到了跃迁几率在相空间中所满足的方程。 As a quasiprobability distribution function in phasespace and a special representation of the density matrix, Wigner function has great significance in physics. In this paper, first, Wigner function’s characteristic and calculation approach are introduced. Then, with Stareigen equation we obtain the Wigner function for threedimensional harmonic oscillator. In the end, we discuss the method describing the interaction between phonons and electrons (or photons) and obtain the equation that transition probability satisfies in phase space.
Abstract: As a quasiprobability distribution function in phasespace and a special representation of the density matrix, Wigner function has great significance in physics. In this paper, first, Wigner function’s characteristic and calculation approach are introduced. Then, with Stareigen equation we obtain the Wigner function for threedimensional harmonic oscillator. In the end, we discuss the method describing the interaction between phonons and electrons (or photons) and obtain the equation that transition probability satisfies in phase space.
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