基于激发态的一维无限深势阱的等谱势

The Potentials Isospectral to Infinite One-dimensional Potential Well Based on Higher Excited States

超对称性量子力学形式可以利用激发态来生成超势,得到广义化超对称形式.利用广义化超对称形式,即使用一维无限深势阱对应的激发态波函数来生成超势,并通过逐次因子化方法,构造出了一系列与一维无限深势阱等能谱的新的势函数,即构造出了一个与一维无限深势阱等能谱的哈密顿量等级系统,而且能够得到该等级系统中所有的哈密顿量的能谱和能量本征函数.

Abstract：In this paper, the formalism of the supersymmetric quantum mechanics is generalized to the cases where the superpotential is generated by higher excited eigenstates. It is shown that generalized supersymmetric forrealism can be used to construct the potentials isospectral to infinite one - dimensional potential well by repeated refactorizations. Obviously, the hierarchy of Hamihonians isospectral to infinite one - dimensional potential well is constructed and the energy eigenvalues and eigenfunctions of the Hamiltonians in the hierarchy are derived.