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In this paper, we calculate the mass spectra of heavy quarkonium by usingmatrix Numerov's method to make the predictions of F and G states for furtherexperiments. The method gives a very reasonable result which is in a goodagreement with other methods and with recently published theoretical data. Fromthe yielded wave functions we calculate the root mean square radius r_ms and\b{eta} coefficients of heavy quarkonium

Theoretical Calculations for Predicted States of Heavy Quarkonium via Non-Relativistic Frame Work