A Coulomb bound state is a physical normalizable eigenfunction for an attractive potential , . For the usual regular boundary condition at the origin its energies are the displayed values, . The spherically symmetric states have orbital angular momentum zero; series-termination quantization of the Coulomb radial equation constructs them as a polynomial times a decaying exponential. Square integrability on the punctured radial interval alone does not replace the physical condition at the origin.
Articles by others on the same topic
A bound state refers to a physical condition in which a particle or system is confined within a potential well or region, resulting in a stable arrangement where it cannot escape to infinity. This concept is prevalent in quantum mechanics, atomic physics, and certain areas of particle physics. ### Key Characteristics of Bound States: 1. **Energy Levels**: In a bound state, the energy of the system is quantized.