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This paper develops a mathematical approach to calculate the
ground state energies of ?pd and ?dt muonic ions. The calculations have been performed by combination of Nikiforov–Uvarov method and linear variational approach. Basis kets have been introduced to expand terms of wave function using a well definition of vector space in the hyper-spherical coordinates. The full calculations have been performed and compared with other variational calculations in the hyper-spherical harmonic formalism. The results of the variational energies show a fast convergence with a relatively small number of candidate basis functions
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