论文标题
量子su $（2 | 1）$ supersymmetric $ \ mathbb {c}^n $ smorodinsky- winternitz系统
Quantum SU$(2|1)$ supersymmetric $\mathbb{C}^N$ Smorodinsky--Winternitz system
论文作者
论文摘要
我们研究了SU $（2 | 1）的量子特性$ supersymmetric（变形$ {\ cal n} = 4 $，$ d = 1 $ supersymmetric）在复杂的Euclidian Space $ \ Mathbb {C}^n $上的可分布性Smorodinsky-Winternitz系统的扩展。构建了完整的波函数，并计算了能量谱。结果表明，su $（2 | 1）$ supersymmetry表示玻色子和费米子状态属于单独的能级，从而表现出光谱的“偶数”分裂。还定义了宽大的隐藏对称操作员，并给出了它们对SU $（2 | 1）$多重功能的动作。考虑了同一系统的等效描述，该系统在超符号su $（2 | 1,1）$量子力学方面被考虑，并且根据SU $（2 | 1,1）$的$（2 | 1,1）的新表示形式。
We study quantum properties of SU$(2|1)$ supersymmetric (deformed ${\cal N}=4$, $d=1$ supersymmetric) extension of the superintegrable Smorodinsky--Winternitz system on a complex Euclidian space $\mathbb{C}^N$. The full set of wave functions is constructed and the energy spectrum is calculated. It is shown that SU$(2|1)$ supersymmetry implies the bosonic and fermionic states to belong to separate energy levels, thus exhibiting the "even-odd" splitting of the spectra. The superextended hidden symmetry operators are also defined and their action on SU$(2|1)$ multiplets of the wave functions is given. An equivalent description of the same system in terms of superconformal SU$(2|1,1)$ quantum mechanics is considered and a new representation of the hidden symmetry generators in terms of the SU$(2|1,1)$ ones is found.
