Another set of infinitely many exceptional (X_{\ell}) Laguerre polynomials
Another set of infinitely many exceptional (X_{\ell}) Laguerre polynomials
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DOI：
10.1016/j.physletb.2009.12.062
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发表时间：
2009-11
影响因子：
4.4
通讯作者：
S. Odake;R. Sasaki
中科院分区：
文献类型：
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作者：
S. Odake;R. Sasaki
我们提出了一个新的无穷多个形状不变位势的集合和相应的例外（X_{\ell}）Laguerre多项式。它们是对最近导出的两组无限多个形状不变因而精确可解的一维量子力学势以及相应的X_{\ell} Laguerre和Jacobi多项式（Odake和Sasaki，Phys. Lett. B679（2009）414-417）。新的X_{\ell} Laguerre多项式和势函数是由已知的X_{\ell} Jacobi多项式和势函数通过一个简单的限幅过程得到的，而已知的X_{\ell} Laguerre多项式和势函数则是由已知的X_{\ell} Jacobi多项式和势函数的镜像以同样的方式得到的.
We present a new set of infinitely many shape invariant potentials and the corresponding exceptional (X_{\ell}) Laguerre polynomials. They are to supplement the recently derived two sets of infinitely many shape invariant thus exactly solvable potentials in one dimensional quantum mechanics and the corresponding X_{\ell} Laguerre and Jacobi polynomials (Odake and Sasaki, Phys. Lett. B679 (2009) 414-417). The new X_{\ell} Laguerre polynomials and the potentials are obtained by a simple limiting procedure from the known X_{\ell} Jacobi polynomials and the potentials, whereas the known X_{\ell} Laguerre polynomials and the potentials are obtained in the same manner from the mirror image of the known X_{\ell} Jacobi polynomials and the potentials.