The equation E=mc² was not "discovered" at a specific moment; rather, it was derived as a consequence of Albert Einstein's theory of special relativity, which was published in 1905. In this theory, Einstein proposed that the laws of physics should be the same in all inertial reference frames and introduced the concept of the constancy of the speed of light in a vacuum. From these postulates, he derived the famous equation E=mc², which relates energy (E) to mass (m) and the speed of light (c).
Now, regarding its use in quantum mechanics, it's important to note that quantum mechanics and relativity are two distinct theories that describe different aspects of the physical world. Quantum mechanics deals with the behavior of subatomic particles and the microscopic world, while relativity explains the behavior of objects on a macroscopic scale and the properties of spacetime.
Although relativity is not directly involved in the study of subatomic particles in quantum mechanics, the equation E=mc² still finds relevance in certain situations. In quantum mechanics, particles can be created or annihilated, and this process involves energy transformations. The equation E=mc² allows us to understand the equivalence between mass and energy and how they can be interconverted.
Additionally, in high-energy physics, where both quantum mechanics and relativity play a role, the equation becomes crucial. The study of particle physics often involves energies where the effects of relativity cannot be ignored. For instance, in particle accelerators, such as the Large Hadron Collider (LHC), particles are accelerated to velocities close to the speed of light, and their energies are incredibly high. In such cases, the equation E=mc² is used to understand the conversion of mass into energy and vice versa, as particles are accelerated or collide.
So, while relativity is not directly involved in the study of subatomic particles in quantum mechanics, the equation E=mc² still has broad implications and finds utility in understanding the relationship between energy and mass in various physical phenomena.