Full calculation of μpd and μdt muonic bound levels: Combination of Nikiforov-Uvarov method and variational approach

This paper develops a mathematical approach to calculate the ground state energies of μpd and μdt 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.