Husimi Operator for Describing Probability Distribution of Electron States in Uniform Magnetic Field Studied by Virtue of Entangled State Representation

For the first time we introduce an operator Δh(γ,ε;κ) for studying Husimi distribution function in phase space (γ,ε) for electron’s states in uniform magnetic field, where κ is the Gaussian spatial width parameter. The marginal distributions of the Husimi function are Gaussian-broadened version of the Wigner marginal distributions. Using the Wigner operator in the entangled state 〈λ| representation we find that Δh(γ,ε;κ) is just a pure squeezed coherent state density operator |γ,ε〉κκ〈γ,ε|, which brings much convenience for studying Husimi distribution, so we name Δh(γ,ε;κ) the Husimi operator. We then derive Husimi operator’s normally ordered form that provides us with an operator version to examine various properties of the Husimi distribution.