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We calculate the ratios of $B$ and $D$ meson decay constants by applying thevariational method to the relativistic hamiltonian of the heavy meson. We adoptthe Gaussian and hydrogen-type trial wave functions, and use six differentpotentials of the potential model. We obtain reliable results for the ratios,which are similar for different trial wave functions and different potentials.The obtained ratios show the deviation from the nonrelativistic scaling law,and they are in a pretty good agreement with the results of the Latticecalculations.Comment: 13 pages, 1 Postscript figur

Ratios ofBandDmeson decay constants in relativistic quark model