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A Coulomb scattering state in quantum mechanics , describes a state of a particle where the particle is subject to Coulomb potential and is not localized to a finite region of space.
In general, Coulomb scattering state is a state in Hilbert Space that corresponds to two or more particles with positive interaction energy , which means, the energy of the system is greater than total energy of each separate particles constituting the system therefore these particles are not bound. The energy spectrum of such scattering state is continuous unlike discrete spectrum of bound states in Coulomb Potential.
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