论文标题
具有方形电势的粒子的量子力学的核心动机重新审查
A didactically motivated reexamination of a particle's quantum mechanics with square-well potentials
论文作者
论文摘要
从教学的角度来看，我们解决了有关方孔潜力的两个问题。第一个问题涉及标准的正当性是否在特征值问题的分析中先验省略垂直段的暂时遗漏是LICIT。我们遵循的绕行答案认为答案考虑了相应特征值问题的分析和数值的梯形电势，然后分析梯形电位坡道的斜率时，该解决方案的行为在极限上的行为变为垂直。第二个问题显然与第一个问题有关，它是否与特征功能及其在电势跳跃点上的第一个衍生物的连续性是否合理，这是启动解决方案过程的先验假设，因为它在潜在的特征本特征值问题的教科书方法中被标准地接受。
We address two questions regarding square-well potentials from a didactic perspective. The first question concerns whether or not the justification of the standard a priori omission of the potential's vertical segments in the analysis of the eigenvalue problem is licit. The detour we follow to find out the answer considers a trapezoidal potential, includes the solution, analytical and numerical, of the corresponding eigenvalue problem and then analyzes the behavior of that solution in the limit when the slope of the trapezoidal potential's ramps becomes vertical. The second question, obviously linked to the first one, pertains whether or not eigenfunction's and its first derivative's continuity at the potential's jump points is justified as a priori assumption to kick-off the solution process, as it is standardly accepted in textbook approaches to the potential's eigenvalue problem.
