Investigating Student Understanding of Perturbation Theory and the Inner Products of Functions
Investigating Student Understanding of Perturbation Theory and the Inner Products of Functions
复制标题
调查学生对微扰理论和函数内积的理解
DOI：
10.1119/perc.2015.pr.057
复制
发表时间：
2015
影响因子：
--
通讯作者：
Peter S. Shaffer
中科院分区：
文献类型：
--
作者：
G. Passante;Paul J. Emigh;Tong Wan;Peter S. Shaffer
我们已经研究了学生可以定性地确定扰动对哈密顿量对本征函数能量的影响的程度。结果表明，许多学生在课堂指导后不能确定一阶校正的一些重要特征。我们研究了这种失败可能源于对内积缺乏理解的可能性。由于摄动通常用图形表示，所以重点在于学生确定用图形表示的函数的内积的能力。在这个过程中，我们发现有些学生甚至在量子力学之外的环境中也找不到内积。
We have investigated the extent to which students can qualitatively determine the effect of perturbations to a Hamiltonian on the energies of the eigenfunctions. The results indicate that after lecture instruction many students cannot determine some important features of the first-order correction. We examine the possibility that this failure may stem from a lack of understanding of the inner product. Since perturbations are often represented graphically, the focus has been on student ability to determine the inner product of functions represented graphically. In the process, we have found that some students are unable to find inner products even in contexts outside of quantum mechanics.