Abstract
In present work, the modified Schrödinger equation (MSE) is analytically solved. The Heavy-Light Mesons (HLM) under modified nonrelativistic quark-antiquark potential, are extended to the symmetries of noncommutative quantum mechanics (NCQM), using the generalized Bopp’s shift method. The energy a spectrum of HLM has been investigated in the framework of the perturbative quantum chromodynamics (PQCD) extended nonrelativistic quark model. The new energy eigenvalues and the corresponding Hamiltonian operator are calculated in the 3-dimensional noncommutative real space phase (NC: 3D-RSP) symmetries. The masses of the scalar, vector, pseudoscalar, and pseudovector for (B, Bs , D and Ds) mesons have been calculated in (NC: 3D-RSP). Moreover, using the perturbation approach, we found that the perturbative solutions of discrete spectrum can be expressed by the parabolic cylinder functions function, Gamma function, the discreet atomic quantum numbers (j, l, s, m) of the ǪǬ state and (the spin independent and spin dependent) parameters (a, b, g, h), in addition to noncommutativity parameters. Furthermore, we have shown that the total complete degeneracy of new energy levels of HLM was changed to become equals to the new value 3n2 instead to the old values n2 in ordinary quantum mechanics. Our obtained results are in good agreement with the already existing literature in NCQM.
Highlights
T It is well known that the study of deferent properties of Heavy-Light Mesons (HLM) has attracted attention from researchers specializing in this field, and in particular, the mass spectra of quarkonium systems as charmonium and bottomonium mesons with the quark-antiquark interaction potential for example and cb, is very important for understanding the structure of hadrons and dynamics of heavy quarks [1,2,3,4,5,6]
Schrödinger equation for HLM such as scalar, vector, pseudoscalar, and pseudovector for ( B, Bs, D and Ds ) mesons under modified nonrelativistic quark-antiquark potential, which is given in Eq (17) by using the generalized Bopp’s shift method and standard perturbation theory
E, E, E nc-ghlm nc-mhlm nc-lhlm m,n, j,l,a,b, g,h for modified Schrödinger equation (MSE) for heavy-light mesons with spin-1 on based on our original results, which presented on the Eqs. (31)
Summary
T It is well known that the study of deferent properties of Heavy-Light Mesons (HLM) has attracted attention from researchers specializing in this field, and in particular, the mass spectra of quarkonium systems as charmonium and bottomonium mesons with the quark-antiquark interaction potential for example (cc,bb,cs,bs,bu) and cb , is very important for understanding the structure of hadrons and dynamics of heavy quarks [1,2,3,4,5,6]. To nonrelativistic quark-antiquark potential, explore the possibility of creating new this has the following form: applications and more profound interpretations in the sub-atomics and Nano. This paper consists of five sections and the organization scheme is given as follows: we briefly review the ordinary SE with nonrelativistic quark-antiquark potential on based ref. In the fourth section, a discussion of the main results is present in addition to determining the new formula of mass spectra of the of HLM ( B , Bs , D and Ds mesons) in (NC: 3D-RSP). 3. SOLUTION OF MODIFIED SCHRÖDINGER EQUATION FOR HLM UNDER MODIFIED NONRELATIVISTIC QUARK-ANTIQUARK POTENTIAL
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