Old quantum theory

• 1. The Quantum Of Action

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  Max Planck stood before the German Physical Society on the 14th of December 1900. He presented a formula that solved the black body radiation problem which had baffled physicists for decades. The solution required energy to be emitted in discrete packets rather than as a continuous stream. Planck called this fundamental unit of action h, now known as Planck's constant. His work marked the birth of quantum theory but he did not initially believe his own discovery represented physical reality. Albert Einstein later applied these ideas to specific heats of solids in 1907. This application brought Planck's abstract concept into the realm of mechanical systems. Peter Debye refined Einstein's model in 1912 with what became known as the Debye model. These early efforts resolved discrepancies between classical thermodynamics and experimental observations at low temperatures.

• 2. Bohr And Sommerfeld Models

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  Niels Bohr published his atomic model in 1913 to explain the hydrogen atom spectrum. John William Nicholson had previously quantized angular momentum as an integer multiple of h-bar. Bohr quoted Nicholson directly in his paper while introducing circular electron orbits. Arnold Sommerfeld extended this framework by allowing elliptical trajectories instead of perfect circles. He introduced space quantization through the z-component of angular momentum. This modification explained fine structure in spectral lines better than Bohr's original circle. The resulting Bohr-Sommerfeld model incorporated quantum degeneracy concepts. Hendrik Lorentz contributed the principle of adiabatic invariance which helped define quantum numbers. Sommerfeld's version remained closer to modern quantum mechanics than Bohr's initial proposal.

• 3. Wilson-Sommerfeld Quantization Rules

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  William Wilson and Arnold Sommerfeld independently proposed a procedure for selecting allowed states. They required that the integral of momentum over one period equals an integer times Planck's constant. This condition applied only to systems where motion could be separated into periodic coordinates. The area enclosed by an orbit in phase space became quantized in units of h. Classical mechanics governed the system except for these specific restrictions. Not every motion was permitted under these rules. Only those satisfying the quantization condition existed physically. The method worked well for integrable systems but failed for chaotic dynamics. It provided a heuristic bridge between classical physics and emerging quantum phenomena.

• 4. Periodic Table And Exclusion Principle

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  Edmund Stoner used old quantum theory to determine the modern form of the periodic table. Wolfgang Pauli formulated the exclusion principle based on Sommerfeld's enhancements to atomic models. These developments explained electron configurations within atoms through discrete energy levels. The theory successfully predicted chemical properties despite its theoretical inconsistencies. Half-integer quantum numbers created confusion when electron spin was discovered. Satyendra Nath Bose developed statistics for bosons alongside Einstein during this era. Hendrik Kramers explained the Stark effect using semiclassical methods. The combination of these insights established the structure of elements as known today.

• 5. BKS Theory Rejection

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  Bohr, Kramers, and John C. Slater promoted their BKS theory in 1924. They treated electromagnetic fields classically while keeping matter quantum mechanical. This approach attempted to reconcile conservation laws with wave-particle duality. The Bothe-Geiger coincidence experiment rejected the theory shortly after its proposal. Experimental evidence showed that energy and momentum were conserved only in individual interactions. The failure of BKS theory signaled the end of attempts to modify classical electromagnetism. It forced physicists to abandon semi-classical compromises entirely. Werner Heisenberg later built upon Kramers' transition probability calculations to create matrix mechanics.

• 6. Transition To Matrix Mechanics

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  Werner Heisenberg published his Umdeutung paper in 1925 reformulating all quantum theory. He used Kramers' Fourier components to describe atomic transitions mathematically. Max Born and Pascual Jordan collaborated with him to develop matrix mechanics. Louis de Broglie introduced wave theory of matter in 1924 as a parallel development. Einstein extended de Broglie's ideas into semiclassical equations for matter waves. Erwin Schrödinger found a complete wave equation in 1926 reproducing old results without ambiguity. Paul Dirac proved both methods predicted identical experimental consequences in 1926. The mathematical formalism was finalized by Dirac and John von Neumann. These developments replaced heuristic rules with rigorous operator algebra.

• 7. Limitations And Chaos

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  The old quantum theory could not calculate spectral line intensities accurately. It failed to explain the anomalous Zeeman effect where electron spin mattered. Chaotic systems like two-electron atoms remained unquantizable under these rules. Trajectories were neither closed nor periodic in such dynamical systems. Joseph Keller updated Bohr-Sommerfeld quantization using Einstein's interpretation in the 1950s. Martin Gutzwiller derived semiclassical ways to quantify chaotic systems from path integrals in 1971. The method only worked for integrable systems according to later analysis. Despite these failures, it successfully described many atomic phenomena before 1925. Modern research continues investigating its semi-classical approximation status today.