论文标题
符号量子力学中的分数有效的夸克 - 易夸克相互作用
Fractional Effective Quark-Antiquark Interaction in Symplectic Quantum Mechanics
论文作者
论文摘要
我们在符号量子力学的形式主义中调查了代表绑定的重型夸克 - 易夸克状态的二维非相互作用的强相互作用系统，在广义分数衍生物的背景下，它被认为是线性的。为此，它在相位空间中以线性电势求解了schrödinger方程。获得解决方案（基态），通过与原始解决方案（Meson $ c \ overline {C} $相比，通过Wigner函数进行分析。确定的本征函数通过Weyl产物和相位空间中的Galilei组表示理论连接到Wigner函数。在某些方面，与波浪函数相比，Wigner函数使观察介子系统的非古典状态变得更加简单。
We investigate within the formalism of Symplectic Quantum Mechanics a two-dimensional non-relativistic strong interacting system that represents the bound heavy quark-antiquark state, where it was considered a linear potential in the context of generalized fractional derivatives. For this purpose, it was solved the Schrödinger equation in phase space with the linear potential. The solution (ground state) is obtained, analyzed through the Wigner function comparing with the original solution, the Airy function for the meson $c\overline{c}$. The identified eigenfunctions are connected to the Wigner function via the Weyl product and the Galilei group representation theory in phase space. In some ways, compared to the wave function, the Wigner function makes it simpler to see how the meson system is non-classical.
