From the Classical to the Quantum Particle in a Box: A Sophomore-Level Applications of Modern Physics Course and Laboratory for Engineers and Scientists

对于许多物理和工程专业的学生来说，从低级物理课程过渡到高级物理课程是很困难的：课程材料变得更加抽象，数学变得更加复杂。然而，美国需要增加获得物理科学和工程学位的学生人数，以满足工业需求，并保持美国在技术创新方面的领导地位。与此同时，我们的课程需要现代化，以便让物理和工程专业的学生接触到最新的理论和应用、最先进的实验设备和当前的计算建模技术。该项目为物理和电气工程专业的学生开设了一门二年级的“现代物理应用”课程和实验室，以架起低水平和高水平课程的桥梁，为学生提供他们所需的分析、建模和实验技能，同时也解决了数学技能方面的弱点。材料科学和纳米科学尤其为解决这些问题提供了极好的背景。正在开发的课程从原子和量子力学开始，建立到纳米级系统，最后涉及固体和器件。应用，如激光、量子点、二极管和超导体，贯穿整个课程。随附的实验室与课堂紧密相连，并说明了经典和量子物理学中的复杂概念，如量子化能级和概率。实验材料用于指导学生编写自己的模拟和执行最先进的实验，以激励和整合课程中所述的理论。实验室项目强调了建模和实验之间的相互作用，这是科学知识进步的核心。完整开发的课程直接解决学生的需求和误解，并提高学生的计算建模技能和对控制半导体和纳米级器件的物理原理的理解。因此，它作为一个跨学科的模式，弥合了低水平和高水平的物理和工程课程之间的差距。该课程开发的成果已提交给物理和工程教育界的期刊和数字档案，并将在AAPT和ASEE的区域和国家会议上进一步传播。

The transition from lower-level to upper-level physics courses is difficult for many physics and engineering students: the course material becomes more abstract, and the mathematics more sophisticated. Yet, the United States needs to increase the number of students who earn physical science and engineering degrees to meet the demand of industry and maintain the country's leadership in technology innovation. At the same time, our curricula needs to be modernized in order to expose physics and engineering students to current theories and applications, state-of-the-art experimental apparatus, and current computational modeling techniques. This project is developing a sophomore-level "Applications of Modern Physics" course and laboratory for both physics and electrical engineering students that bridges the lower-level and upper-level curriculum and gives students the analytical, modeling, and experimental skills they need, while also addressing weaknesses in mathematical skills. Materials science and nano-science in particular provide an excellent context in which to address these issues. The course being developed starts from the atom and quantum mechanics, builds up to nano-scale systems, and finally addresses solids and devices. Applications, such as lasers, quantum dots, diodes, and superconductors, are interwoven throughout the course. The accompanying laboratory is closely tied to the class and illustrates complex concepts such as quantized energy levels and probabilities within both classical and quantum physics. The laboratory materials serve to guide students in writing their own simulations and in performing state-of-the-art experiments that motivate and incorporate the theory addressed in the course. The laboratory program highlights the interplay between modeling and experiment that is central to the advancement of scientific knowledge. The fully developed course directly addresses the needs and misconceptions of students, and it increases students' computational modeling skills and understanding of the physical principles that govern semiconductor and nano-scale devices. It thus serves as an interdisciplinary model for bridging the gap between the lower-level and the upper-level curriculum in physics and engineering. Results from this curricular development are being submitted to journals and digital archives of the physics and engineering education communities, and further dissemination is to occur at regional and national meetings of the AAPT and ASEE.