正交多项式的量子力学
Quantum mechanics with orthogonal polynomials
摘要：
提出了一种基于正交多项式的量子力学公式。波函数在位形空间中展开到一组完备的平方可积基上，展开系数为能量的正交多项式。有关相应的物理系统（结构和动力学）的信息来自这些多项式的属性。我们证明了这种公式的一个优点是，精确可解的非相对论性量子力学问题的类别比传统公式中的大（例如，参见本文中的表1）。
英文摘要：
We present a formulation of quantum mechanics based on orthogonal polynomials. The wavefunction is expanded over a complete set of square integrable basis in configuration space where the expansion coefficients are orthogonal polynomials in the energy. Information about the corresponding physical systems (both structural and dynamical) are derived from the properties of these polynomials. We demonstrate that an advantage of this formulation is that the class of exactly solvable non-relativistic quantum mechanical problems becomes larger than in the conventional formulation (see, for example, Table 1 in the text).
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