量子力学中超对称性破缺的新可能性和二阶不可约达布变换
New possibilities for supersymmetry breakdown in quantum mechanics and second order irreducible Darboux transformations
摘要：
本文描述了一维Schroedinger方程的新型不可约二阶达布变换。这种变换的主要特点是变换函数的本征值大于初始（或参考）哈密顿量的基态能量。当这种变换表示为两个一阶变换的链时，中间势是奇异的，因此中间哈密顿量不可能是厄米特的，而最终势是正则的，最终哈密顿量是厄米特的.基于这种变换的二阶导数超对称量子力学模型同时表现出精确和破缺超对称模型的固有性质。
英文摘要：
New types of irreducible second order Darboux transformations for the one dimensional Schroedinger equation are described. The main feature of such transformations is that the transformation functions have the eigenvalues grater then the ground state energy of the initial (or reference) Hamiltonian. When such a transformation is presented as a chain of two first order transformations, an intermediate potential is singular and therefore intermediate Hamiltonian can not be Hermitian while the final potential is regular and the final Hamiltonian is Hermitian. Second derivative supersymmetric quantum mechanical model based on a transformation of this kind exhibits properties inherent to models with exact and broken supersymmetry at once.
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