Discrepancies from Asymptotic Series and Their Relation to Complex Classical Trajectories.
Discrepancies from Asymptotic Series and Their Relation to Complex Classical Trajectories.
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DOI：
10.1103/physrevlett.41.1141
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发表时间：
1978-10
影响因子：
8.6
通讯作者：
R. Balian;G. Parisi;A. Voros
中科院分区：
文献类型：
--
作者：
R. Balian;G. Parisi;A. Voros
存在函数F(X)，当以固定的x和最优阶计算时，其渐近展开式似乎收敛到一个明显偏离F(X)本身的数值。给出了几个例子，表明这种现象并不是例外，应该出现在量子理论中。特别是，在大量子数下，四次振子V=x4能级的半经典展开出现了这样的差异，我们定量地解释为空间和时间坐标变得复杂的经典轨迹的贡献。
There exist functions F (x) whose asymptotic expansions, when computed at fixed x and optimal order, seem to converge to a numerical value which deviates significantly from F (x) itself. Several examples are given, showing that this phenomenon is not exceptional, and should occur in quantum theory. In particular, the semiclassical expansion, at large quantum numbers, of levels of the quartic oscillator V= x 4 presents such discrepancies, which we explain quantitatively as contributions from classical trajectories for which space and time coordinates become complex.