Old Quantization, Angular Momentum, and Nonanalytic Problems

• URL: http://arxiv.org/abs/2009.01014v1
• Date: Mon, 31 Aug 2020 19:35:25 GMT
• Title: Old Quantization, Angular Momentum, and Nonanalytic Problems
• Authors: Nelia Mann and Jessica Matli and Tuan Pham
• Abstract summary: We show that old quantization leads to qualitatively and quantitatively useful information about systems with spherically symmetric potentials. We analyze systems with logarithmic and Yukawa potentials, and compare the results of old quantization to those from solving Schrodinger's equation.
• Score: 1.933681537640272
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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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