In quantum mechanics, physical observables, such as position, momentum, energy, and angular momentum, are represented by mathematical operators. These operators act on the wave function of a quantum system to yield observable quantities when they are applied. For example, the position operator gives the position of a particle, the momentum operator gives the momentum, and so on.
Operators in quantum mechanics are used to calculate expectation values, which are the average values of physical observables in a given quantum state. By using operators, we can perform calculations to determine the probabilities of different measurement outcomes and understand the behavior of quantum systems.
The use of operators allows us to describe the peculiar nature of quantum phenomena, such as superposition, entanglement, and the uncertainty principle. Operators help us analyze the evolution of quantum systems over time and make predictions about the outcomes of measurements.
So, it is essential to employ operators in quantum mechanics to describe, analyze, and predict the behavior of quantum systems. They are an integral part of the mathematical framework that underlies the theory.