Quantum mechanics is generally considered to be a probabilistic theory rather than a deterministic one. It provides a mathematical framework for describing the behavior of microscopic particles, such as electrons and photons, and their interactions.
One of the fundamental principles of quantum mechanics is the uncertainty principle, which states that there are inherent limitations to simultaneously knowing certain pairs of physical properties, such as position and momentum, with precision. This principle introduces inherent randomness and probabilistic behavior into the theory.
Quantum mechanics uses mathematical entities called wavefunctions to describe the state of a quantum system. The wavefunction evolves over time according to the Schrödinger equation, which is a deterministic equation. However, when it comes to making measurements or observations of a quantum system, the theory provides probabilities for the outcomes. The probabilities are determined by the wavefunction through a process known as wavefunction collapse or wavefunction reduction, which occurs during the measurement process.
The probabilistic nature of quantum mechanics is deeply rooted in the mathematics and has been extensively validated by experimental observations. It has been confirmed through numerous experiments, such as the famous double-slit experiment, which demonstrates the wave-particle duality of quantum entities and the probabilistic nature of their behavior.
It's worth noting that there are interpretations of quantum mechanics that attempt to provide different philosophical perspectives on the nature of quantum randomness and its relationship to underlying deterministic processes. However, the core mathematical formalism of quantum mechanics itself is probabilistic in nature.