Abstract
Niels Bohr finished his studies at the University of Copenhagen in 1911 with a thesis on the magnetic properties of metals. In September of the same year he went to Cambridge to continue his studies at the famous Cavendish Laboratories with Thomson. Thomson received him cordially and seemed to be interested in the work of the young Dane. However, in the literature one can find the cryptic remark that their communication was hampered by language barriers; maybe Thomson’s knowledge of Danish was only rudimentary ...While Bohr still had to grapple with these difficulties, Rutherford visited Cambridge and reported on his new insights concerning the structure of atoms. Bohr was fascinated by Rutherford and decided to move to Manchester. To the surprise of many colleagues soon also Rutherford was quite impressed by Bohr. This was not necessarily to be expected because in general Rutherford did not have a very favourable opinion of “pure” theoreticians. After all, he had not needed a theoretician to deduce the structure of atoms from the scattering experiments in Manchester. When asked why he made an exception for Bohr, he is reported to have said: “Bohr is different, he is a football player.”
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- 1.
We use the Heaviside system commonly employed in particle physics (see Appendix A for a detailed description) where the dimensionless fine-structure constant\(\alpha \simeq 1/137.036\) has the form \(\alpha = e^2/(4\pi \,\hbar \,c)\) with \(\hbar = h/2\pi \).
- 2.
The quanta are a hopeless mess.
- 3.
Heisenberg’s new paper that will appear soon looks very mystical but is certainly correct and profound.
- 4.
In the so-called momentum space the roles of X and P would have to be interchanged.
- 5.
The square brackets denote the antisymmetric product (commutator) of two operators.
- 6.
Given the extraordinary differences of starting points and concepts of Heisenberg’s quantum mechanics on the one hand and the “wave-like” or “physical” mechanics, recently presented here with its main features, on the other hand, it is quite strange that these two quantum theories agree with each other in all presently known results even where they deviate from the old quantum theory ...This is indeed very remarkable because starting point, viewpoints, method, the whole mathematical apparatus actually seem to be completely different.
- 7.
In full generality the potential can also depend on time: \(V(t,{\vec {r}})\).
- 8.
Note added in proof: a more detailed consideration shows that the probability is proportional to the square of the wave function.
- 9.
However, it does not seem to be justified to me that it is generally referred to as Copenhagen interpretation.
- 10.
One can look at the world with the p-eye and one can look at it with the x-eye, but if you want to open both eyes at the same time you go crazy.
- 11.
...Your letter keeps circulating here and Bohr, Dirac, Hund and I keep fighting over it.
- 12.
...it is shown that canonically conjugate quantities can simultaneously be determined with a characteristic uncertainty only.
- 13.
- 14.
The experiment was performed by Stern and Gerlach in 1922, three years before the actual introduction of spin. At that time it was actually interpreted as strong support for the Bohr–Sommerfeld model. The history of the experiment and of its reception can be found in Pakvasa (2018).
- 15.
All charged particles have nonvanishing mass.
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Ecker, G. (2019). The Path to Quantum Mechanics. In: Particles, Fields, Quanta. Undergraduate Lecture Notes in Physics. Springer, Cham. https://doi.org/10.1007/978-3-030-14479-1_3
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