模型原子的微扰电离
Ionization of a Model Atom by Perturbations of the Potential
摘要：
本文研究了受$δ$ -函数势束缚的粒子在随时间变化的束缚强度（参数激发）作用下的波函数随时间的演化。这个模型的简单性允许某些非微扰计算进行分析，在一个和三个维度。因此，在强度为$r$且持续时间为$t$的脉冲之后，结合态$|θ(t)|^2$的存活概率表现为$|θ(t)|^2 -|θ(\infty)|^2 \sim t^{-α}$，其中$θ(\infty)$和$α$均取决于$r$。另一方面，强短脉冲序列在中间时间尺度上产生指数衰减。
英文摘要：
We study the time evolution of the wave function of a particle bound by an attractive $δ$-function potential when it is subjected to time dependent variations of the binding strength (parametric excitation). The simplicity of this model permits certain nonperturbative calculations to be carried out analytically both in one and three dimensions. Thus the survival probability of bound state $|θ(t)|^2$, following a pulse of strength $r$ and duration $t$, behaves as $|θ(t)|^2 -|θ(\infty)|^2 \sim t^{-α}$, with both $θ(\infty)$ and $α$ depending on $r$. On the other hand a sequence of strong short pulses produces an exponential decay over an intermediate time scale.
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