论文标题
旧量化，角动量和非分析问题
Old Quantization, Angular Momentum, and Nonanalytic Problems
论文作者
论文摘要
我们探讨了应用于非零角动量状态的旧量化方法，并表明它会导致有关具有球体对称电位的系统的定性和定量有用的信息。首先，我们回顾了该模型在氢中的传统应用，并讨论爱因斯坦 - 布里林 - 面包师量化解决旧量化状态与真实量子机械状态之间的不匹配的方式。然后，我们分析了具有对数和Yukawa电位的系统，并将旧量化的结果与解决Schrodinger方程的系统进行比较。我们表明，旧的量化技术可洞悉与给定主量子数相关的能级的传播，并为能量提供定量准确的近似值。以这种方式分析系统涉及多种数值方法的有价值的综合，并提供了对经典机械物理和量子机械物理之间联系的更深入的见解。
We explore the method of old quantization as applied to states with nonzero angular momentum, and show that it leads to qualitatively and quantitatively useful information about systems with spherically symmetric potentials. We begin by reviewing the traditional application of this model to hydrogen, and discuss the way Einstein-Brillouin-Keller quantization resolves a mismatch between old quantization states and true quantum mechanical states. We then analyze systems with logarithmic and Yukawa potentials, and compare the results of old quantization to those from solving Schrodinger's equation. We show that the old quantization techniques provide insight into the spread of energy levels associated with a given principal quantum number, as well as giving quantitatively accurate approximations for the energies. Analyzing systems in this manner involves an educationally valuable synthesis of multiple numerical methods, as well as providing deeper insight into the connections between classical and quantum mechanical physics.
