A search for shape-invariant solvable potentials
A search for shape-invariant solvable potentials
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寻找形状不变的可解势
DOI：
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发表时间：
1989
期刊：
影响因子：
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通讯作者：
G. Lévai
中科院分区：
文献类型：
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作者：
G. Lévai
本文研究了一种构造势函数的简单方法，它与Bhattacharjie和Sudarshan（1962）的工作有关，并且薛定谔方程可以用已知的特殊函数来求解。结果表明，这种方法可以与超对称量子力学联系起来，并且这种关系可以帮助确定满足线性齐次二阶微分方程的哪些特殊函数可以成为势函数为V（x）= W ~ 2（x）-W ′（x）的薛定谔方程的解。作者以正交多项式为例说明了这一过程，并得到了一类形状不变势的波函数的显式表达式。
The author investigates a simple method of constructing potentials which is related to the work of Bhattacharjie and Sudarshan (1962) and for which the Schrodinger equation can be solved in terms of known special functions. It turns out that this method can be related to supersymmetric quantum mechanics and this relationship can help to decide which special functions, satisfying linear homogeneous second-order differential equations, can be solutions of the Schrodinger equation with potentials of the form V(x)=W2(x)-W'(x). The author illustrates this procedure with the example of orthogonal polynomials and obtains explicit expressions of wavefunctions of a wide class of shape-invariant potentials.