应用物理学专业本科毕业论文.docVIP

PAGE 3 应用物理学专业本科毕业论文 精确量子化条件中若干问题的研究 学生姓名：薄红亮 学 号：0409010210 指导教师：崔燕岭 专　　业：应用物理学 年　　级：04-2班 学　　校：河南理工大学 精确量子化条件中若干问题的研究 摘 要 量子化条件是连接经典和量子力学世界的桥梁，传统的Bohr量子化条件、Bohr-Sommerfeld量子化条件、WKB量子化条件分别在一定条件下适用，后来提出的精确量子化条件对于一维束缚态问题严格成立，可以用来计算具有形状不变势的量子系统的本征能级，并获得了较多的应用。但是传统的量子条件对于非经典区并不成立。我们把精确的量子化条件推广到了全空间，也就是包含了经典禁区在内的区间。利用此种方法，研究了双势阱、一维谐振子、氢原子等系统。结果表明，在非经典区间的情况与经典区大不相同，原来的Nπ项变成了一个依赖于具体模型的量。 关键词： 量子化条件 非经典区 不变量 PACC： 0365 1130 Some Topics on Exact Quantization Rule Abstract Quantization condition is the bridge from classical mechanics to quantum mechanics. The traditional Bohr quantization condition, Bohr-Sommerfeld quantization condition and WKB quantization condition hold approximately under certain conditions. The exact quantization condition exactly holds for the one-dimensional bound states, which can be used to calculate the eigenenergy levels of the quantum systems with the shape invariant potentials, and widely used in many areas. However, the traditional quantization conditions do not hold for the non-classical areas. The exact quantization condition is generalized to the whole space, including the classical forbidden area. The generalized expression is used to study in the double-trap, one-dimensional harmonic oscillator, and hydrogen systems. The results showed that the corrected terms becomes eigenenergy levels depended and the original N π term also models depended. Keywords：quantization condition, non-classical area, invariant, quantization rule PACC： 0365，1130 目　　录 TOC \o 1-3 \h \z \u HYPERLINK \l _Toc201479957 1 引 言 PAGEREF _Toc201479957 \h 1 HYPERLINK \l _Toc201479958 2 量子化的历史 PAGEREF _Toc201479958 \h 3 HYPERLINK \l _Toc201479959 1.1 普朗克量子理论 PAGEREF _Toc201479959 \h 3 HYPERLINK \l _Toc201479960 1.2 爱因斯坦的光量子理论 PAGEREF _Toc201479960 \h 3 HYPERLINK \l _Toc201479961 1.3 玻尔的光量子理论 PAGEREF _Toc201479961 \h 4 HYPERLINK \l _Toc201479962 1.3.1 经典理论遇到的困难 PAGEREF _Toc201479962 \h 4 HYPERLINK \l _Toc201479963 1.3.2 玻尔-索末菲的量子化条件 PAGEREF _Toc20