超几何型方程的形状不变性和升降算子
Shape invariance, raising and lowering operators in hypergeometric type equations
摘要：
薛定谔方程可以用相关的特殊函数精确求解，它与超几何型方程理论中定义的一些自伴算子直接相关。基本公式发生在一个超对称的方法，这些哈密顿是后果的一些公式有关的一般理论相关联的特殊功能。利用这种联系，我们得到了Schr odinger方程的一般理论，并推广了某些特殊势情形下的某些已知结果.
英文摘要：
The Schr\" odinger equations which are exactly solvable in terms of associated special functions are directly related to some self-adjoint operators defined in the theory of hypergeometric type equations. The fundamental formulae occurring in a supersymmetric approach to these Hamiltonians are consequences of some formulae concerning the general theory of associated special functions. We use this connection in order to obtain a general theory of Schr\" odinger equations exactly solvable in terms of associated special functions, and to extend certain results known in the case of some particular potentials.
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