Applied Research Of WKB Approximation In Meson Spectrum

In quantum physics,the interaction between particles can be described by potential energy functions,and the physical properties of the system are often explained by relativistic and non-relativistic wave equations.In the past decades,many potential energy functions that play an important role in describing physical phenomena have been proposed.However,there are few wave equations with potential energy functions with exact solutions,so people use approximate solutions and numerical methods to obtain their solutions.In the context of quark model,we use WKB approximation to study Killingbeck potential.The implicit approximate solution of the energy eigenvalue of Schrodinger equation is obtained by using appropriate quantization conditions and three kinds of complete elliptic integrals.In the double meson system,we use Minuit software to fit the parameters in the Killingbeck potential.In the last decade,a series of excited states of B_c,c(?) and b(?) double heavy mesons systems have been observed experimentally.Based on the theoretical framework of these newly discovered excited states and WKB approximation methods,we systematically study the energy spectra of B_c,c(?) and b(?) double heavy mesons families and show that our results agree well with experimental values except for a few states.At the same time,we predict the highly excited states of B_c,c(?) and b(?) double heavy mesons,which are not found in the experiment,and hope that these theoretical predictions can provide help to find their mass in the future.Finally,the Killingbeck potential is compared with the screening potential in MGI model.The results show that the Killingbeck potential is similar to the screening potential,and the Killingbeck potential can also suppress the mass of the highly excited state.It helps us to understand the role of quark interaction potential in highly excited states and the application range of double mesons in Killingbeck potential.