The Husimi function for electron distributions

Abstract

We discuss the properties of a phase space distribution function that can be expressed as a Gaussian convolution of the Wigner function corresponding to the oneelectron charge density matrix for a many-electron system. This distribution function is known as the Husimi function. It is real and nowhere negative and can be interpreted as a probability density for finding an electron in a particular coherent state or, equivalently, for finding it in a region of phase space consistent with the uncertainty principle. Information is not lost in the transformation from the Wigner function, which can be recovered. We discuss the relationships among various functions and their Fourier transforms. The Husimi function does not have the ordinary densities as marginals but rather Gaussian convolutions of them, from which the ordinary densities can be recovered. Advantages of the Husimi function over the Wigner function for the interpretation of electronic structure are discussed. Illustrative results for the hydrogen atom and for the nitrogen atom at the SCF level are presented.