Quantum mechanics provides a mathematical framework for calculating the probabilities of different outcomes for quantum systems. These probabilities are represented by wavefunctions, and the evolution of these wavefunctions is described by the Schrödinger equation.

One of the key differences between classical mechanics and quantum mechanics is the concept of superposition. In classical mechanics, particles have a definite state, like a definite position and momentum, but in quantum mechanics, particles can exist in many states simultaneously. Only when an observation is made will the wavefunction collapse to a single state.

Another important concept in quantum mechanics is uncertainty. The Heisenberg uncertainty principle states that it is impossible to simultaneously know the exact position and momentum of a particle with absolute precision. This limitation is a fundamental aspect of the quantum world.

Quantum mechanics has many practical applications, including quantum computing, quantum cryptography, and quantum teleportation. Additionally, many aspects of our understanding of physics, such as the nature of the electromagnetic force and the behavior of black holes, can only be properly understood within the framework of quantum mechanics.