In quantum mechanics, the terms "continuum state" and "bound state" describe different types of energy states that a quantum object can occupy.
A bound state refers to a state in which a quantum object is confined within a certain region or potential well. The object is trapped by a potential barrier, such as an atom bound to its nucleus or an electron confined to an atom's energy levels. Bound states have discrete energy levels, often referred to as energy eigenstates, and the object remains localized.
On the other hand, a continuum state refers to a state where the quantum object is not confined and has access to a continuous range of energy levels. In this case, the energy spectrum is continuous rather than discrete. A quantum object in a continuum state is not bound by a potential well or localized to a specific region.
To provide some examples:
In the context of atomic physics, an electron in a bound state within an atom occupies discrete energy levels, forming the familiar electron shells. These bound states correspond to stable and confined orbits around the atomic nucleus.
In contrast, when an electron gains sufficient energy to overcome the binding potential of an atom, it can enter a continuum state. This occurs, for example, when electrons are ionized and become free particles. In the continuum state, the electron is no longer localized to the atom and can occupy a range of energy levels.
It's important to note that the classification of states into bound or continuum states depends on the specific system and potential under consideration. In some cases, the boundary between bound and continuum states may be blurred, such as in the case of quasi-bound states, which exhibit characteristics of both bound and continuum states.
Overall, the distinction between bound states and continuum states in quantum mechanics is based on whether a quantum object is confined and possesses discrete energy levels (bound state) or is not confined and has a continuous energy spectrum (continuum state).