In quantum mechanics, a bound state refers to a state of a particle or a system of particles that is confined within a finite region of space due to the presence of a potential energy well or a binding force. In such a state, the total energy of the system is negative, indicating that the bound system is stable.
A bound state can be understood by considering the Schrödinger equation, which describes the behavior of quantum systems. When a particle is subject to a potential energy function, the Schrödinger equation allows for certain solutions where the particle's wavefunction is localized and does not extend to infinity. These localized wavefunctions represent the bound states of the system.
In a bound state, the particle or particles are trapped within a potential energy well, which prevents them from freely propagating or escaping to infinity. This confinement results in quantized energy levels, where the energy of the bound system is discretized, with only specific allowed energy values. These discrete energy levels are often referred to as energy eigenstates.
Bound states are typically observed in systems such as atoms, molecules, and nuclei, where the electromagnetic or nuclear forces act as binding forces. In these systems, the negatively charged electrons are bound to the positively charged nucleus due to the attractive electromagnetic force, forming stable atomic or molecular structures.
It is worth noting that the concept of bound states extends beyond single particles and can also apply to systems of multiple particles, such as molecules or nuclei. In these cases, the bound state arises from the collective interaction between the particles, resulting in a stable and confined system.