论文标题
库仑和环形的总和的klein-fock-gordon方程的近似解决方案
Approximate Solutions to the Klein-Fock-Gordon Equation for the sum of Coulomb and Ring-Shaped like potentials
论文作者
论文摘要
我们考虑了带有质量$ m $的无旋转相对论粒子运动的量子机械问题，由klein-fock-gordon方程与等量表$ s（\ vec {r}）$和vector $ v（\ vec {r}）$ coulomb $ coulomb plus环形电位。结果表明，所考虑的系统在$ \ left | e \ right | <mc^{2} $和$ \ left | e \ right |> mc^{2} $ engiels y yermy Spectra的关注| <mc^{2} $中具有离散。我们找到相应完整波函数的分析表达式。构建了径向波动方程的动态对称组$ su（1,1）$。该组发电机的代数使以纯粹的代数方式找到能量光谱。还表明，在限制$ c \ to \ infty $中，波函数，能量光谱和组发生器的相对论表达式进入了非依赖性问题的相应表达式。
We consider the quantum mechanical problem of the motion of a spinless charged relativistic particle with mass$M$, described by the Klein-Fock-Gordon equation with equal scalar $S(\vec{r})$ and vector $V(\vec{r})$ Coulomb plus ring-shaped potentials. It is shown that the system under consideration has both a discrete at $\left|E\right|<Mc^{2} $ and a continuous at $\left|E\right|>Mc^{2} $ energy spectra. We find the analytical expressions for the corresponding complete wave functions. A dynamical symmetry group $SU(1,1)$ for the radial wave equation of motion is constructed. The algebra of generators of this group makes it possible to find energy spectra in a purely algebraic way. It is also shown that relativistic expressions for wave functions, energy spectra and group generators in the limit $c\to \infty $ go over into the corresponding expressions for the nonrelativistic problem.
