论文标题
量子衰变定律的分析：量子隧穿真的指数吗？
Analysis of quantum decay law: Is quantum tunneling really exponential?
论文作者
论文摘要
自1928年首次推导以来，指数衰减定律已经建立了很好的确立，但是这不是确切的，而只是一个大致的描述。近年来，已经记录了一些非指数衰减的实验和理论指示。首先，我们通过分析时间依赖时间依赖性的schrödinger方程在一个维度上，用于由无限壁和具有有限宽度的矩形屏障组成的电势，并通过将其视为平方电位的顺序，并具有切割的谐波振荡器电位。然后，使用交错的Leap-Frog方法，我们解决了时间依赖的Schrödinger方程，以获得切割的谐波振荡器电位。在这两种方法中，分析了粒子和衰减参数λ的生存概率的时间依赖性。该结果表现出在短时和中间时间的生存概率的非指数行为。
The exponential decay law is well established since its first derivation in 1928, however it is not exact but only an approximate description. In recent years some experimental and theoretical indications for non-exponential decay have been documented. First we solve analytically the time-dependent Schrödinger equation in one dimension for a potential consisting of an infinite wall plus a rectangular barrier with finite width and also a cut harmonic oscillator potential by considering it as a sequence of square potentials. Then using the staggered Leap-Frog method, we solve the time-dependent Schrödinger equation for the cut harmonic oscillator potential. In both methods, time dependence of the survival probability of the particle and the decay parameter λ are analyzed. The results exhibit non-exponential behavior for survival probability at short and intermediate times.
