nt - p h / 06 11 20 6 v 1 2 0 N ov 2 00 6 Husimi operator and Husimi function for describing electron ’ s probability distribution in uniform magnetic field

For the first time we introduce the Husimi operator ∆ h (γ, ε; κ) for studying Husimi distribution in phase space (γ, ε) for electron's states in uniform magnetic field, where κ is the Gaussian spatial width parameter. Using the Wigner operator in the entangled state λ| representation we find that ∆ h (γ, ε; κ) is just a pure squeezed coherent state density operator |γ, ε κκ γ, ε| , which brings convenience for studying and calculating the Husimi distribution. We in many ways demonstrate that the Husimi distributions are Gaussian-broadened version of the Wigner distributions. Throughout our calculation we have fully employed the technique of integration within an ordered product of operators.