In quantum mechanics, the concept of a "free state" refers to a state of a particle or system that is not subject to any external forces or potentials. It is a fundamental concept used to simplify the analysis and understanding of quantum systems.
A free state is often characterized by a state vector that evolves over time according to the Schrödinger equation or a similar equation of motion. This evolution describes how the state of the system changes in time without the influence of external factors. In other words, the particle or system in a free state is not affected by any potential energy barriers or forces acting upon it.
Mathematically, a free state is typically represented as a superposition of momentum eigenstates, where each eigenstate corresponds to a definite momentum value. These momentum eigenstates form a complete basis for describing the particle's state. By expressing the system in terms of momentum eigenstates, one can easily analyze and calculate various properties, such as probabilities, energy spectra, and scattering processes.
It is important to note that in real-world scenarios, truly isolated systems that are completely free from external influences are rare. However, the concept of a free state serves as a valuable approximation that simplifies the understanding of quantum systems and provides a foundation for more complex calculations and analysis.