According to the principles of quantum mechanics, the quantum state of a system is determined by a combination of factors, including the initial conditions of the system and the interactions it undergoes. The evolution of a quantum system is governed by the Schrödinger equation, which describes how the wave function of the system changes over time.
The initial state of a quantum system is typically specified as a wave function, which is a mathematical representation of the probability amplitudes associated with different possible outcomes of measurements on the system. The wave function contains all the information about the system's quantum state.
As the system interacts with its environment or other systems, the wave function evolves according to the laws of quantum mechanics. This evolution can include processes such as superposition (where the system exists in a combination of multiple states) and entanglement (where the states of multiple systems become correlated).
When a measurement is made on a quantum system, the wave function "collapses" into one of the possible measurement outcomes. The probability of each outcome is determined by the squared magnitude of the corresponding probability amplitude in the wave function. The specific outcome that is observed is probabilistic, and the probabilities are determined by the quantum state of the system before the measurement.
In summary, the quantum state of a system is determined by a combination of the system's initial conditions and its interactions, and the evolution of the state is described by the Schrödinger equation. The act of measurement causes the wave function to collapse into one of the possible measurement outcomes, with the probabilities determined by the quantum state prior to measurement.