常规和超对称JWKB公式的精确性及Stokes图的全局对称性
Exactness of Conventional and Supersymmetric JWKB Formulae and Glo bal Symmetries of Stokes Graphs
摘要：
结果表明，一维量子力学中JWKB公式精确量子化能级的情况是两个势及其对应的Stokes图的本质上是一个整体对称性的结果。也就是说，这是后者在空间变量的复平面上平移的不变性，即势和斯托克斯图必须是周期性的。基本周期带（平行四边形）中转折点的扩散是JWKB公式精确性的另一个限制。对满足适当条件的单阱势类进行了系统的分析。只有十个潜力（一个或两个真正的参数）量化精确的JWKB公式已被发现，所有这些都符合（或等价于）与众所周知的发现以前。还表明超对称JWKB公式的精确性是常规公式的相应精确性的结果，反之亦然。由于后两个确切的JWKB量子化的潜力已经另外建立。这些结果表明，精确的超对称JWKB公式选择的孔泰形式与超对称破缺与否无关。还证明了势的形不变性与它们在x平面上的亚纯结构之间的密切关系。
英文摘要：
It has been shown that the cases of the JWKB formulae in 1--dim QM quantizing the energy levels exactly are results of essentially one global symmetry of both potentials and their corresponding Stokes graphs. Namely, this is the invariance of the latter on translations in the complex plain of the space variable i.e. the potentials and the Stokes graphs have to be periodic. A proliferation of turning points in the basic period strips (parallelograms) is another limitation for the exactness of the JWKB formulae. A systematic analyses of a single-well class of potentials satisfying suitable conditions has been performed. Only ten potentials (with one or two real parameters) quantized exactly by the JWKB formulae have been found all of them coinciding (or being equivalent to) with the well-known ones found previously. It was shown also that the exactness of the supersymmetric JWKB formulae is a consequence of the corresponding exactness of the conventional ones and vice versa. Because of the latter two exactly JWKB quantized potentials have been additionally established. These results show that the exact SUSY JWKB formulae choose the Comtet at al form of them independently of whether the supersymmetry is broken or not. A close relation between the shape invariance property of potentials considered and their meromorphic structure on the x-plane is also demonstrated.
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