Old Quantum Mechanics by Bohr and Sommerfeld from a Modern Perspective

• URL: http://arxiv.org/abs/2506.00408v6
• Date: Tue, 22 Jul 2025 21:10:15 GMT
• Title: Old Quantum Mechanics by Bohr and Sommerfeld from a Modern Perspective
• Authors: Kamal K. Barley, Andreas Ruffing, Sergei K. Suslov,
• Abstract summary: We review Bohr's atomic model and its extension by Sommerfeld from a mathematical perspective of wave mechanics.<n>The derivation of quantization rules and energy levels is revisited using semiclassical methods.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We review Bohr's atomic model and its extension by Sommerfeld from a mathematical perspective of wave mechanics. The derivation of quantization rules and energy levels is revisited using semiclassical methods. Sommerfeld-type integrals are evaluated by elementary techniques, and connections with the Schr\"{o}dinger and Dirac equations are established. Historical developments and key transitions from classical to quantum theory are discussed to clarify the structure and significance of the old quantum mechanics.

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