The implanted muon can form a quantum-coherent resonant state when sandwiched between two I=1/2 fluorine ions, where I is the nuclear spin. This state has usually only been for I=1/2 nuclei which have no quadrupole moment. This proposal seeks to explore a newly-discovered analogous state in compounds with the A15 structure containing either V (I=7/2) and Nb (I=9/2) in order to understand the nature of the muon site in A15 compounds. Preliminary data on V3Si has yielded a promising hint of a quantum coherent state with I>1/2 nuclei. Knowledge of this state, in which quadrupolar coupling can play a role, may provide a new route through which muons could be used in the future to study charge density waves via the electric field gradient at I>1/2 nuclei.