论文标题
交替的Wentzel-Kramers-brillouin近似与Schrödinger方程：重新发现了Bremmers系列及以后
Alternating Wentzel-Kramers-Brillouin Approximation to the Schrödinger Equation: Rediscover the Bremmers series and beyond
论文作者
论文摘要
我们提出了用于求解Schrödinger方程的Wenzel-Kramers-brillouin（WKB）近似的扩展。一组耦合的微分方程是通过考虑具有辅助条件的WAVE函数的ANSATZ来获得其第一个衍生物的。结果表明，交替的扰动方法可以将微分方程的集合解散，从而产生众所周知的布雷默序列，而且，由于幅度的改善，可以通过一系列递归对角色来完善波浪函数的相位。因此，我们发现了一个一般的量化公式，其中编码了几何形状样物理。每当差分反射系数和经典动量的比率保持恒定时，我们表明我们的一般量化公式将减少到与通过重新点击扰动WKB系列获得的结果相符的封闭形式量化条件，并将其降低。
We propose an extension of Wenzel-Kramers-Brillouin (WKB) approximation for solving the Schrödinger equation. A set of coupled differential equations is obtained by considering an ansatz of the wave function with an auxiliary condition on gauging its first derivative. It is shown that the alternating perturbation method can decouple the set of differential equations, yielding the well know Bremmer series, and in addition, by virtue of improvement on amplitudes, can refine the phase of the wave function in a sequence of recursive diagonalizations. We therefore find a general quantization formula in which the geometric-optical-like physics is encoded. Whenever the ratio of the differential reflection coefficient and the classical momentum remains constant, we show that our general quantized formula will reduce to the closed-form quantization condition that agrees with the result obtained by re-summation the perturbative WKB series to all orders.
