In quantum mechanics, the behavior of particles and systems is indeed described by probabilistic or statistical principles. The theory provides a framework for calculating the probabilities of different outcomes when measuring observable properties of particles, such as their position or momentum.
Regarding initial conditions, they play a crucial role in determining the probabilities and outcomes of measurements in quantum mechanics. The state of a quantum system at a given time is described by its wave function, which contains information about the probabilities of different possible outcomes. The wave function evolves over time according to the Schrödinger equation, which is the fundamental equation of quantum mechanics.
The specific form of the wave function at the initial time, often referred to as the initial condition, influences the subsequent evolution of the system. However, unlike classical physics, where knowledge of the initial conditions would allow precise predictions of future states, in quantum mechanics, the evolution is probabilistic.
Quantum mechanics introduces inherent uncertainty, even with complete knowledge of the initial conditions. This uncertainty is encapsulated in the concept of wave function collapse, which occurs when a measurement is made on the system. The measurement process selects one of the possible outcomes with a probability determined by the system's wave function.
In summary, while initial conditions are important in quantum mechanics and can influence the probabilities of different outcomes, the theory introduces inherent probabilistic behavior that goes beyond classical determinism. The role of initial conditions is to provide the starting point for the evolution of the wave function, which then determines the probabilities of measurement outcomes.