Husimi operator and Husimi function for describing electron's probability distribution in uniform magnetic field derived by virtue of the entangled state representation

Abstract: For the first time we introduce the Husimi operator Delta_h(gamma,varepsilon;kappa) for studying Husimi distribution in phase space(gamma,varepsilon) for electron's states in uniform magnetic field, where kappa is the Gaussian spatial width parameter. Using the Wigner operator in the entangled state |lambda> representation [Hong-Yi Fan, Phys. Lett. A 301 (2002)153; A 126 (1987) 145) we find that Delta_h(gamma,varepsilon;kappa) is just a pure squeezed coherent state density operator |gamma,varepsilon>_kappa kappa<gamma,varepsilon|, 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.