The Wigner function represents a quantum state as a quasi-probability distribution in phase space, expressed in terms of position and momentum. It provides insight into quantum behavior and nonclassical effects such as interference. This overview highlights its key representations and properties.

The hydrogen atom is a cornerstone of quantum mechanics, traditionally described in three dimensions. Interestingly, its two-dimensional counterpart—where the electron’s motion is confined to a plane—also admits an analytical solution. This overview summarizes that solution.

The Madelung equations reformulate the Schrödinger equation—one of the foundations of quantum mechanics—into a hydrodynamic form that describes the flow of a nonclassical fluid. This overview revisits their derivation and key ideas.