In quantum mechanics, what quantity yields the probability density for an electron's location?

The square of the wave function ($\Psi^2$)

The location of an electron in an atom is fundamentally probabilistic, described by quantum mechanics rather than deterministic classical paths. The mathematical description that captures this likelihood is the wave function, symbolized by the Greek letter Psi ($\ ext{Psi}$). The physical interpretation of this function relates directly to measurable probability density. Specifically, it is the square of the wave function ($\ ext{Psi}^2$) that provides the probability density distribution. Where $\ ext{Psi}^2$ is high, the electron is highly likely to be found if a measurement were taken; where it is zero, the electron will never be found. This concept is crucial because it directly maps the fuzzy cloud shape onto a quantifiable probability map, forming the atomic orbital.