The Position Operator is a fundamental concept in quantum mechanics, representing the observable quantity of a particle's position in space. It is denoted by the symbol \hatx and acts on the wave function of a quantum system. When applied, it provides information about where a particle is likely to be found upon measurement. In mathematical terms, the Position Operator is defined in the context of a Hilbert space, where it operates on state vectors. Its eigenvalues correspond to possible position measurements, while the associated eigenstates represent the states of the system at those positions. This operator is crucial for understanding the behavior of particles, such as electrons, in quantum systems.