旧量子化、Angular Momentum和非分析问题
Old Quantization, Angular Momentum, and Nonanalytic Problems
摘要：
我们探讨了旧的量子化方法，适用于非零角动量的状态，并表明，它导致定性和定量有用的信息系统与球对称的潜力。我们首先回顾了这个模型在氢原子上的传统应用，并讨论了Einstein-Brillouin-Keller量子化解决旧量子化态和真实量子力学态之间不匹配的方法。然后，我们分析系统的对数和汤川势，并比较旧的量子化的结果，从解决薛定谔方程。我们发现，旧的量子化技术提供了深入了解与一个给定的主量子数，以及给定量准确的近似能量的能级的传播。以这种方式分析系统涉及多种数值方法的教育价值合成，以及对经典和量子力学物理之间的联系提供更深入的了解。
英文摘要：
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.
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