In quantum mechanics, the terms "free state" and "bound state" refer to different types of energy states that a particle can occupy within a potential energy well.
Free State: A free state refers to a state in which a particle is not confined by any potential energy barrier or force. In other words, it is not bound to any specific region or system. A particle in a free state can move freely in space and has sufficient energy to escape from any localized potential. Examples of free states include a free electron in vacuum or a particle moving in an unconfined region without any external influences.
Bound State: A bound state, on the other hand, refers to a state in which a particle is confined within a potential energy well. It is typically associated with a negative energy, which allows the particle to be trapped within the region of the potential. The particle is bound to the system and cannot escape without the input of additional energy. Examples of bound states include electrons orbiting around an atomic nucleus or the vibrational and rotational states of molecules.
The distinction between free states and bound states is important in understanding the behavior and properties of particles in various physical systems. Bound states are typically characterized by quantized energy levels, while free states have continuous energy spectra. Bound states also play a crucial role in phenomena such as the formation of stable atoms and the existence of energy levels in solid-state materials, while free states are often associated with particles involved in scattering or propagation through space.