Yes, quantum mechanics is consistent with Einstein's mass-energy equivalence formula E=mc^2. In fact, quantum mechanics provides a deeper understanding of the relationship between energy and mass.
In quantum mechanics, particles are described by wave functions that obey specific equations, such as the Schrödinger equation or the Dirac equation. These equations incorporate the concept of energy and mass through their mathematical formulations.
In the context of these equations, particles have an associated energy operator and a mass operator. The energy operator corresponds to the total energy of the particle, including its rest energy (mc^2) and any additional energy due to motion or interaction with other particles. The mass operator corresponds to the intrinsic mass of the particle.
The mass-energy equivalence is reflected in the quantum mechanical equations through the interaction between the energy and mass operators. When particles are at rest, their total energy operator reduces to the rest energy operator (mc^2), which is proportional to their mass. This corresponds to the familiar formula E=mc^2.
It's important to note that quantum mechanics goes beyond the simple E=mc^2 equation by providing a more detailed description of particle behavior, such as wave-particle duality and the quantization of energy levels. Nonetheless, the fundamental principle of mass-energy equivalence is upheld within the framework of quantum mechanics.