论文标题
关于所谓的费米在量子力学中的黄金法则，包括绝热之后的新观点
New Perspectives on the so-called Fermi's Golden Rule in Quantum Mechanics including Adiabatic Following
论文作者
论文摘要
提出了一个新颖且容易理解的黄金法则依赖性扰动理论的推导。该推导基于所用扰动的绝热打开，例如在散射理论的一些形式发展中。节能是根据直觉和物理吸引力的洛伦兹线形状表示的，而不是人工振荡性罪（x）= x类型线形状，这些线形状出现在常规派生中。衍生物有效性的条件紧凑，方便地在频率/能量域而不是在通常的时域中表达。该推导还强调了如何忠实，即时地遵循扰动电位的正方形的变化，就像人们在绝热极限中所期望的那样。首先，像往常一样，通过单个指数时间变化来实现绝热的打开。但是，我们证明了通过过渡速率瞬时的扰动电势的正方形之后是更笼统的，并且可以为一般变化的时间依赖的扰动而得出一般的黄金法则。这允许人们得出最初由Weisskopf和Wigner的经典论文得出的简单衰减定律的概括。提供了这项经典作品本质的教程解释。审查了将黄金法则应用于问题（例如原子的电场电离）的Oppenheimer方法，其中扰动潜力也可以创建最终状态。与量子力学中绝热定理的原始衍生物相比，不需要使用能量隙条件来得出我们对绝热行为的结果。
A novel and readily understandable derivation of the Golden Rule of time dependent perturbation theory is presented. The derivation is based on adiabatic turning on of the perturbation as used, for instance, in some formal developments of scattering theory. Energy conservation is expressed in terms of an intuitively and physically appealing Lorentzian line shape rather than the artificial, oscillatory sin(x)=x type line shape that appears in conventional derivations. The conditions for the derivation's validity are compactly and conveniently expressed in the frequency/energy domain rather than in the usual time domain. The derivation also highlights how, along with energy conservation, the transition rate faithfully and instantaneously follows the variations in the square of the perturbing potential as one may expect in the adiabatic limit. In the first instance, the adiabatic turning on is achieved, as usual, by a single exponential time variation. But we demonstrate that the instantaneous following of the square of the perturbing potential by the transition rate is more general and that one can derive the Golden Rule for a general slowly varying time dependent perturbation. This allows one to derive generalisations of the simple decay law, originally derived in the classic paper by Weisskopf and Wigner; a tutorial exposition of the essence of this classic work is provided. The Oppenheimer method for applying the Golden rule to problems, such as the electric field ionisation of atoms, in which the perturbing potential can also create the final states, is reviewed. No use of an energy gap condition is needed to derive our results on adiabatic behaviour in contrast to the origianl derivations of the adiabatic theorem in quantum mechanics.
