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As we all known that non-relativistic or semi-relativistic constituent quarkmodels can describe a large number of the meson sand baryon properties withsurprising accuracy. In this work, we studied Killingbeck potential by usingWKB approximation in the constituent quark model. The implicit approximatesolution of the energy eigenvalue of the Schr\"{o}dinger equation is obtainedby using appropriate quantization conditions. Under the Killingbeck potentialwith the WKB approximation, we studied the spectra of double heavy mesons andpredict the masses of high excited states in $c\bar{c}$, $b\bar{b}$ and$b\bar{c}$ families. Finally, we discuss the application scope of double heavymesons in Killingbeck potential.

WKB approximation under Killingbeck potential and its application to double heavy meson mass spectrum