Abstract
This chapter contains the background and the essential publications for the development of matrix mechanics from 1919 to 1925. The path leads from Born’s suggestion in 1919 that the space-time continuum looses its meaning on the quantum scale to the implementation of discontinuous quantum transitions (“Quantensprünge”) in 1924, when the term “Quantum Mechanics” (“Quantenmechanik”) is introduced. In June 1925 Born and Jordan introduce discontinuous “quantum vectors” (“Quantenvektoren”)—which will later become “matrix elements”—to combine Einstein’s elementary Quantum Optics with Born’s “Quantenmechanik”. Heisenberg’s “reinterpretation paper” (“Umdeutung”) of 1925 introduces matrix multiplication rules for the “quantum vectors”, which are used by Born and Jordan in September 1925 to achieve the final breakthrough: Commutation relations and quantum equations of motion. The “three men’s paper” (“Dreimännerarbeit”) of Born, Heisenberg, Jordan of November 1925 completes the formal development of matrix mechanics.
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Notes
- 1.
not to be confused with the paper of September 1925, later called BJ-2.
- 2.
Born and Jordan use gothic letters to indicate vector quantities, as was usual in Germany at the time.
- 3.
Both had been students of Sommerfeld to obtain their doctorates in Munich, and both went to Göttingen afterwards to work with Born.
- 4.
After an extensive stay at MIT, further lectures were given at other universities (Chicago, Wisconsin, Berkeley, Cal-Tech., Columbia); thereby the new message about quantum theory arrived in the US very quickly after its conception.
- 5.
The criticism of Born’s “heavy mathematics” was partly understandable; occasionally it did occur that the physical content was somewhat buried in the mathematical formulation and difficult to extract.
- 6.
Concerning Born’s attitude towards Pauli and Heisenberg, the letter to Einstein of 7 April 1923 contains: “I had Heisenberg here during the winter.....equally as gifted as Pauli... but nicer and more pleasant”.
- 7.
Pauli’s publications on the Compton effect (Z. Phys. 18, 272, 1923, and Z. Phys. 22, 261, 1924) relied on Einstein’s light quanta , in disagreement with Bohr’s continuous radiation. Pauli’s letter of 12 Dec 1924 to Bohr (containing the manuscript of the “Pauli principle”, Z. Phys 31, 765, 1925) criticized Bohr’s continuous orbits; Pauli expressed his support of Born’s concept about discontinuous quantum transitions , characterizing stationary states only by quantum numbers.
- 8.
Field quantization will obtain wider recognition only after Dirac’s stay in Göttingen from May to September 1926, from where he moved on to Copenhagen, and Dirac’s publication on field quantization (Proc. R. Soc. Lond. A 114, 243–265, 1927) carried out in Copenhagen afterwards.
- 9.
At MIT Born gave 20 lectures on Quantum Theory, followed by 10 lectures on Lattice Theory. These lectures were written up and published quickly by MIT (Max Born: Problems of Atomic Dynamics). Born’s lectures at MIT were followed by visits of other Universities (Chicago, Wisconsin, Berkeley, Cal-Tech., Columbia), where further lectures were given.
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Capellmann, H. (2017). The Quantum Theory of Born, Heisenberg, and Jordan. In: The Development of Elementary Quantum Theory. SpringerBriefs in History of Science and Technology. Springer, Cham. https://doi.org/10.1007/978-3-319-61884-5_5
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DOI: https://doi.org/10.1007/978-3-319-61884-5_5
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