Quantum mechanics is inherently a probabilistic theory. It provides a mathematical framework for describing the behavior of particles and systems on the microscopic scale, where the properties of particles are described by wavefunctions.
According to the principles of quantum mechanics, the wavefunction of a particle contains all the information about its possible states. However, when a measurement is made on a quantum system, the outcome is not deterministically predicted. Instead, the theory provides probabilities for different measurement outcomes.
The probabilistic nature of quantum mechanics arises from the wave-particle duality and the uncertainty principle. The wavefunction of a particle evolves according to the Schrödinger equation, which is deterministic. However, when a measurement is made, the wavefunction "collapses" to a particular state, and the outcome is one of the possible eigenvalues of the observable being measured, each with its associated probability.
The probabilities in quantum mechanics are given by the Born rule, which states that the probability of obtaining a specific measurement result is proportional to the squared magnitude of the corresponding component of the wavefunction. This probabilistic interpretation is a fundamental aspect of quantum mechanics and has been confirmed by numerous experimental observations.
It's important to note that while the individual measurement outcomes are probabilistic, the overall statistical behavior of a large number of identical measurements can be predicted with high accuracy. This is known as the statistical interpretation of quantum mechanics, where the probabilities manifest as regular patterns when many measurements are performed on identical systems.
In summary, quantum mechanics is a probabilistic theory that describes the behavior of particles and systems in terms of probabilities for measurement outcomes.