sh（2/2）超代数本征态与广义超相干态和超压缩态
sh(2/2) Superalgebra eigenstates and generalized supercoherent and supersqueezed states
摘要：
超代数本征态（SAES）的概念，然后应用到寻找SAES与$sh(2/2)$超代数，也被称为海森堡-Weyl李超代数。这意味着要求解一个格拉斯曼特征值超方程。因此，$sh(2/2)$ SAES包含与超对称谐振子相关的超相干态类，也包含与$osp(2/2) \sdir sh(2/2)$超代数相关的超压缩态类，其中$osp(2/2)$表示由海森堡-外尔李超代数生成元的二次乘积形成的算子集生成的正交辛李超代数。研究了这些态的性质，并与应用群论技术得到的态进行了比较。此外，还得到了新的广义超相干态和超压缩态。作为应用，构造了没有定义Grassmann宇称和等谱的超厄米哈密顿量和$η$ --伪--超厄米哈密顿量.计算了它们的本征态和相应的超相干态。
英文摘要：
The superalgebra eigenstates (SAES) concept is introduced and then applied to find the SAES associated to the $sh(2/2)$ superalgebra, also known as Heisenberg--Weyl Lie superalgebra. This implies to solve a Grassmannian eigenvalue superequation. Thus, the $sh(2/2)$ SAES contain the class of supercoherent states associated to the supersymmetric harmonic oscillator and also a class of supersqueezed states associated to the $osp(2/2) \sdir sh(2/2)$ superalgebra, where $osp(2/2)$ denotes the orthosymplectic Lie superalgebra generated by the set of operators formed from the quadratic products of the Heisenberg--Weyl Lie superalgebra generators. The properties of these states are investigated and compared with those of the states obtained by applying the group-theoretical technics. Moreover, new classes of generalized supercoherent and supersqueezed states are also obtained. As an application, the superHermitian and $η$--pseudo--superHermitian Hamiltonians without a defined Grassmann parity and isospectral to the harmonic oscillator are constructed. Their eigenstates and associated supercoherent states are calculated.
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