Deep Research
Lecture Materials: The Birth of Quantum Mechanics
Lecture notes tracing the birth of quantum mechanics from Planck's blackbody law through the Bohr model, matrix mechanics, and the Schrödinger equation.
Lecture materials The birth of quantum mechanics
Chapter:
1900 - The birth of
QM?
1913 - Bohr's atomic
model
until 1922 - Bohr-Sommerfeld
era
until 1925 - Zeeman
crisis
1924/25 - Incoherent light scattering on atoms
(dispersion)
1925/26 -
breakthrough
1924-26 - wave
mechanics\
:::::::::::::: {#goog-gt-tt .skiptranslate dir="ltr"}
::::: {style="padding: 8px;"}
:::: {}
::: logo
{width="20"
height="20"}
:::
::::
:::::
::: {.top style="padding: 8px; float: left; width: 100%;"}
Original text {#original-text .title .gray}
:::
:::: {.middle style="padding: 8px;"} ::: original-text ::: ::::
:::::: {.bottom style="padding: 8px;"} ::: activity-links [Contribute a better translation]{.activity-link}[]{.activity-link} :::
:::: started-activity-container
::: activity-root ::: :::: ::::::
::: {.status-message style="display: none;"} ::: ::::::::::::::
introduction .pdf\
[1900 - The birth of summary Black body radiation (courtesy MPIWG) .pdf
QM?]{#planck1900}
**Willy Vienna - *About energy distribution in the emission spectrum of a black body* (Ann. Phys. 294, 662 (1896)).** [.pdf](https://uni-tuebingen.de/fileadmin/Uni_Tuebingen/Fakultaeten/MathePhysik/Institute/IAP/Forschung/MOettel/Geburt_QM/wien_AnnPhys_294_662_1896.pdf)\
[Vienna leads its radiation law with somewhat daring arguments *du (ν) \~ ν^3rd^e^-^*const. *ν / (kT) dν* from. He uses it for this the Maxwell Boltzmann speed distribution in an
ideal gas and the assumption that a gas molecule at a certain speed *v* even radiation of a certain frequency *ν (v)* sends out.]{.small}\
**Max Planck - *About irreversible radiation processes* (Ann. Phys. 306, 69 (1900))** [.pdf](https://uni-tuebingen.de/fileadmin/Uni_Tuebingen/Fakultaeten/MathePhysik/Institute/IAP/Forschung/MOettel/Geburt_QM/planck_AnnPhys_306_69_1900.pdf)\
[Invoices for an electrical resonator in a thermal radiation field. The damping of the Resonators are only performed by radiation. Deriving the relationship between resonator energy
*U* and energy density of the radiation field *u*. With a certain assumption for entropy of the resonator *S (U)* Planck derives the Vienna Radiation Act, with the conviction that
this is the only possible form.]{.small}\
**Max Planck - *Entropy and temperature of radiant heat* (Ann. Phys. 306, 719 (1900))** [.pdf](https://uni-tuebingen.de/fileadmin/Uni_Tuebingen/Fakultaeten/MathePhysik/Institute/IAP/Forschung/MOettel/Geburt_QM/planck_AnnPhys_306_719_1900.pdf)\
[Lummer and Pringsheim (Physikalisch-Technische Reichsanstalt, today PTB) have black body radiation measured with significant deviations from the Vienna Radiation Act. Planck is not
convinced because others Measurements of passports still match this. He brings another entropy argument, which in his opinion, the Vienna Radiation Act confirmed as the only possible
form. This fallacy based on the assumption that already *a* Resonator is sufficient for entropy *S (U)* to determine correctly.]{.small}\
**Otto Lummer and Ernst Pringsheim - *About the radiation of the black body for long waves* (Negotiations of the German Physical Society. 2, 163 (1900))** [.pdf](https://uni-tuebingen.de/fileadmin/Uni_Tuebingen/Fakultaeten/MathePhysik/Institute/IAP/Forschung/MOettel/Geburt_QM/lummer.pdf)\
[The latest data in the long-wave area convincingly prove the deviations from the Vienna Radiation Act. Criticism of Vienna\'s \`\` handwaving \'\' and Planck\'s \`\` unambiguous \'\'
entropy.]{.small}\
**Max Planck - *About an improvement in Vienna\'s radiation equation* (Negotiations of the German Physical Society. 2, 202 (1900)).** [.pdf](https://uni-tuebingen.de/fileadmin/Uni_Tuebingen/Fakultaeten/MathePhysik/Institute/IAP/Forschung/MOettel/Geburt_QM/planck_VerhDPG_2_202_1900.pdf)\
[Planck has accepted that the data speak against the Vienna Radiation Act. He presents a \`\` guessed \'\' entropy *S (U)*that establishes the Planck Radiation Act.]{.small}\
**Max Planck - *About the law of energy distribution in the normal spectrum* (Ann. Phys. 309, 553 (1901)).** [.pdf](https://uni-tuebingen.de/fileadmin/Uni_Tuebingen/Fakultaeten/MathePhysik/Institute/IAP/Forschung/MOettel/Geburt_QM/planck_AnnPhys_309_553_1901.pdf)\
[Planck now looks at an ensemble of *N* Resonators that he in *P* Energy levels divided to then operate Boltzmann statistics. The width of the energy levels *hν* but finally he
leaves! The Proportionality constant *H* (for \`\` auxiliary size \'\') is the quantum of action. With that he comes on the new entropy function *S (U)*that leads to Planck\'s
Radiation Act. Hooray!]{.small}\
[1913 - Bohr's atomic Joseph John Thomson - On the Structure of the Atom: an Investigation of the Stability and Periods of Oscillation of a number of Corpuscles arranged at equal intervals around the .pdf
model]{#bohr1913} Circumference of a Circle; with Application of the Results to the Theory of Atomic Structure (Philosophical Magazine Series 6 7, 239 (1904)).
[J.J.Thomson\'s \`\` raisin cake model \'\' places electrons (raisins) in a uniformly positively charged sphere (cake batter). Light emission takes place through vibrations of the
electrons around their equilibrium position. The work characterizes something tiring these vibrations, quantitative success remains compared to the known emission spectra fails.
Nevertheless, subsequent physicists work on this model.]{.small}\
**Ernest Rutherford - *The scattering of α and β particles by matter and the structure of the atom* (Philosophical Magazine Series 6 21, 669 (1911)).** [.pdf](https://uni-tuebingen.de/fileadmin/Uni_Tuebingen/Fakultaeten/MathePhysik/Institute/IAP/Forschung/MOettel/Geburt_QM/rutherford_PhilMag_21_669_1911.pdf)\
[This somewhat tough work contains the famous calculation for the cross-section of the scattering of two point charges. Rutherford then compares the effect of scattering on a central
charge with the effect of scattering on Thomson\'s atomic model (point electrons + diffuse positive charge within a sphere). Only the former model seems to be able to reasonably
describe the existing scatter data.]{.small}\
**J. W. Nicholson - *The constitution of the solar corona* (Monthly Notices of the Royal Astronomical Society 72, 677 (1912)).** [.pdf](https://uni-tuebingen.de/fileadmin/Uni_Tuebingen/Fakultaeten/MathePhysik/Institute/IAP/Forschung/MOettel/Geburt_QM/nicholson_mnras_72_677_1912.pdf)\
[Nicholson tries to adjust the frequencies in the star spectra to energy differences in a Rutherford-like atomic model (but without reference to Rutherford). His model consists of a
positive one Central cargo *no* and *n* Electrons on a common circular path (\`\` nebulium \'\' *n*=4, \`\` protofluorine \'\' *n*=5). Compared to the data, he recognizes that the
angular momentum of the stationary railways is quantized must! (Page 679)]{.small}\
**Niels Bohr - *On the constitution of atoms and molecules* (Philosophical Magazine Series 6 26, 1 (1913)).** [.pdf](https://uni-tuebingen.de/fileadmin/Uni_Tuebingen/Fakultaeten/MathePhysik/Institute/IAP/Forschung/MOettel/Geburt_QM/bohr_PhilMag_26_1_1913.pdf)\
[Bohr accepts the two premises: (1) the atom consists of a positively charged point-shaped core and negatively charged point-shaped electrons and (2) light is emitted in quanta of
energy *hν*. His first conclusion and working hypothesis is (page 7): classic mechanics apply to equilibrium states in the atom, however the classic theory does not apply to
transitions, but only the Planck formula. The discrete equilibrium states for a one-electron system are with the *ad hoc*Condition (equation (2)) *W (ν) = nhν / 2* derived, where *ν*
the orbital frequency is that of the orbit with the total energy *W (ν)* heard. *n* is the main quantum number. Bohr can now explain the known series of the hydrogen atom. The *ad
hoc*condition is now derived using the correspondence principle (page 13 ff.): Circulation frequency of the electron and transition frequency between adjacent lanes must be the same
for large quantum numbers as due to the classic ones Electrodynamics expected. - Except for the famous Bohr box sets, this is a great and incredibly clear work!]{.small}\
[until 1922 - Arnold Sommerfeld - Atomic construction and spectral lines (1921). .pdf
Bohr-Sommerfeld
era]{#bohr-sommerfeld}
[Sommerfeld\'s classic text of 600 pages in the second edition from 1921.]{.small}\
**Arnold Sommerfeld - *To the quantum theory of the spectral lines* (Annals of Physics 356, 1 (1916) and 356, 125 (1916)).** [.pdf (I)](https://uni-tuebingen.de/fileadmin/Uni_Tuebingen/Fakultaeten/MathePhysik/Institute/IAP/Forschung/MOettel/Geburt_QM/sommerfeld_AnnPhys_356_1_1916.pdf)\
[.pdf (II)](https://uni-tuebingen.de/fileadmin/Uni_Tuebingen/Fakultaeten/MathePhysik/Institute/IAP/Forschung/MOettel/Geburt_QM/sommerfeld_AnnPhys_356_125_1916.pdf)\
[Sommerfeld demonstrates the fertility of the Bohr quantization approach using a detailed treatment the elliptical orbits of a particle in the central field. As a postulate, he puts
that everyone is canonical Degree of freedom should be quantized. With regard to Epstein (1916), he discusses that suitable canonical coordinates are those in which the Jacobian
function separates. He also demonstrates that at Consideration of relativistic effects in the kinetic energy of the particle the degeneration in relation to the two quantum numbers
*n* and *n \'*that to the canonical variables *φ* and *r*belong, is lifted. This leads to a splitting of the spectral lines (fine structure). The results are in good Consistency with
the experiment. It is also amazing that the fine structure formula found here is also in accordance with the Dirac theory for an electron in the central potential. This contains the
effect of spin orbit coupling and the Darwin term, which it uses in Sommerfeld\'s treatment of course not there. However, the Dirac energy levels only depend on the total angular
momentum, so it exists still degeneration in terms of spin and web angular momentum.]{.small}\
**Niels Bohr - *On the quantum theory of line spectra* (Kgl. Danskde Vid. Selsk, Skr. nat.-math. Afd., 8. Raekke IV. (1918)).** [.pdf (22 MB)](https://uni-tuebingen.de/fileadmin/Uni_Tuebingen/Fakultaeten/MathePhysik/Institute/IAP/Forschung/MOettel/Geburt_QM/bohr_KglDanske_8RIV_1_1918.pdf)\
[This work is a kind of status report on the basics of quantum theory worked out up to that point. Be discussed. (i) Adiabate invariance (Honorary Festival 1916): the quantized energy
levels remain unchanged, even if, for example, the harmonic oscillator becomes inharmonic. (ii) Quantization of quasi-periodic Systems via the Jacobian effect function (Epstein 1916).
Now the so-called play Effect variables (generalized impulses that are all constant and the characteristic frequencies *ω* of the system represent) and angle variables (generalized
coordinates, all proportional *ωt*are) a big role. In general, each coordinate can be in one Fourier series can be developed in the angle variables. This wording is the starting point
for many subsequent work.]{.small}\
**Johannes Stark - *Observations about the effect of the electric field on spectral lines* Ann. Phys. 348, 965 (1914), Parts I and 353, 193 (1915), Part V.** [.pdf (I)](https://uni-tuebingen.de/fileadmin/Uni_Tuebingen/Fakultaeten/MathePhysik/Institute/IAP/Forschung/MOettel/Geburt_QM/stark_AnnPhys_348_965_1914.pdf)\
[.pdf (V)](https://uni-tuebingen.de/fileadmin/Uni_Tuebingen/Fakultaeten/MathePhysik/Institute/IAP/Forschung/MOettel/Geburt_QM/stark_AnnPhys_353_193_1915.pdf)\
[Description of the groundbreaking experiment (part I), quantitative results (part V).]{.small}\
**Johannes Stark - *Leader of physics?***
[Wikipedia biography]{.small}\ [link](http://de.wikipedia.org/wiki/Johannes_Stark)
[Article in *Black corps* about so-called \`\` white Jews \'\' (1937)]{.small}\ [.html](https://uni-tuebingen.de/fileadmin/Uni_Tuebingen/Fakultaeten/MathePhysik/Institute/IAP/Forschung/MOettel/Geburt_QM/stark_weisse_juden_1937.html)
**Paul Epstein - *The theory of the strong effect* (Ann. Phys. 355, 489 (1916)).** [.pdf](https://uni-tuebingen.de/fileadmin/Uni_Tuebingen/Fakultaeten/MathePhysik/Institute/IAP/Forschung/MOettel/Geburt_QM/epstein_AnnPhys_355_489_1916.pdf)\
[Solution of the Kepler problem with an additional homogeneous electric field in *x*-Direction through parabolic coordinates. The solutions are quasi-periodic (Librations), the
quantization regulations are expanded accordingly (see the work from Bohr and Sommerfeld).]{.small}\
[until 1925 - Zeeman Woldemar Voigt - Further on the expansion of the coupling theory of the Zeeman effects (Ann. Phys. 346, 403 (1913)).\ .pdf
crisis]{#zeeman} The abnormal Zeeman effects of the D-type spectral linins (Ann. Phys. 347, 210 (1913)). .pdf\
[Amazingly, both normal and abnormal Zeeman effects can be completely classic \`\` be understood \". The frequency shift in the normal Zeeman effect corresponds to the Larmor
frequency with which the classic orbit around the magnetic field axis specifies (Lorentz, 1897). This leads to the triplet splitting of a line. One observes the abnormal Zeeman effect
a 4- or 6-fold splitting of the Balmer lines already split by the fine structure. Voigt explains this by different precession frequencies of a system of coupled and harmonic bound
electrons. For that *H*-Atom, of course, makes little sense, but this seems reasonable for elements with a higher atomic number. For this scon the fine structure splitting is also
considerably larger than that of *H*-Atom.]{.small}\
**Arnold Sommerfeld - *Quantum theoretical reinterpretation of Voigt\'s theory of the abnormal Zeeman effect of the D-line type* (Z. Phys. 8, 257 (1922)).** [.pdf](https://uni-tuebingen.de/fileadmin/Uni_Tuebingen/Fakultaeten/MathePhysik/Institute/IAP/Forschung/MOettel/Geburt_QM/sommerfeld_zphys_8_257_1922.pdf)\
[The explanation of the transition of anomalous Zeeman is also attractive about Voigts theory for the snack effect. Sommerfeld writes the Voigt formulas for the transition frequencies
around in energy leva shifts. In this form they also appear again when you the abnormal Zeeman effect with a disorder-theoretical treatment of the Dirac equation calculates (Darwin,
1928). It\'s almost a miracle.]{.small}\
**Alfred Landé - *About the abnormal Zeeman effect* (Z. Phys. 5, 231 (1921)).** [.pdf](https://uni-tuebingen.de/fileadmin/Uni_Tuebingen/Fakultaeten/MathePhysik/Institute/IAP/Forschung/MOettel/Geburt_QM/lande_zphys_5_231_1921.pdf)\
[The country that endures the times *g*Factor (the normal Zeeman split multiplied) is introduced here and then based on the available experimental results simply guessed. This
requires a new quantum number, which according to today Understanding the total angular momentum (sum of orbital angular momentum and spin).]{.small}\
**Werner Heisenberg - *To the quantum theory of the line structure and the abnormal Zeeman effects* (Z. Phys. 8, 273 (1922)).** [.pdf](https://uni-tuebingen.de/fileadmin/Uni_Tuebingen/Fakultaeten/MathePhysik/Institute/IAP/Forschung/MOettel/Geburt_QM/heisenberg_zeeman_1922.pdf)\
[Heisenberg\'s first work, at the age of 20 and as the sole author. He shares the overall angular momentum of an atom with *Z* Electrons on in 1/2 (rotary momentum of the atomic
fuselage with *Z*-1 Electrons) and the rest (remaining angular momentum of the residual electron). With a little good will modern readers discover the spin-orbit coupling and a
reasonably consistent quantization of both Spin as well as the total angular momentum, at least in the case of small magnetic fields. However, to connect to the Voigt summer field
formulas for any magnetic field strength Heisenberg had to find that Swivel pulse of the fuselage always along the sum of the outer magnetic field and the orbital magnetic field of
the electron. This assumption now violated the quantization rules and the semi-classical Selection principle, i.e. at the heart of quantum theory at that time. As a result, Landé
complained to SommerfeldPauli didn\'t like the broken quantum numbers (then why not other fractions?) and Bohr commented diplomatically that Heisenberg\'s assumptions were difficult
to justify. The success justifies the means, Heisenberg said, in fact it should be until 1926 no other, reasonably reasonable quantum model of the abnormal Zeeman effect.]{.small}\
[1924/25 - Incoherent light [The intensity of the light scattering could be measured relatively well on diluted gases, and theoretical efforts focused on using the correspondence principle reasonably consistent
scattering on atoms theory based on the interaction of a classic radiation field with a Find `` classic '' quantized atom. Heisenberg did this very strongly in the creation of his 1925s Work
(dispersion)]{#dispersion} influenced.]{.small}\
**Niels Bohr, Hendrik Kramers and John Slater - *The quantum theory of radiation* (Philosophical Magazine Series 6 47, 785 (1924)).** [.pdf](https://uni-tuebingen.de/fileadmin/Uni_Tuebingen/Fakultaeten/MathePhysik/Institute/IAP/Forschung/MOettel/Geburt_QM/bks_PhilMag_47_785_1924.pdf)\
[Slater came to Copenhagen on a scholarship in 1924 to discuss the following ideas:\
1. Emission and absorption of radiation takes place according to Einstein\'s photon concept.\
2nd An emitted photon is \"carried\" by a classic field so that interference is possible.\
3rd Even if there is currently no emission process, there is this classic field, to which all atoms in the system contribute. This field contains all frequencies in which the atoms
can emit and absorb. The Probability for such an emission or absorption process is determined by the corresponding one Fourier component in the field.\
4th The field is not generated by the mechanical movement of the electron, but by (virtual) movements with the Emission and absorption frequencies. The dynamics of the equally virtual
field still have to be determined in order to eliminate the probability aspect under 3.\
Bohr did not want to accept the physical existence of photons (especially because of the impossibility of interference from him Opinion), so point 1. has been deleted. As a
consequence, it was now unable to define emission and absorption processes give more that are subject to energy and impulse conservation. Bohr now concluded that Preservation of
energy and momentum only on a statistical averageapply. The article is now one pure prose text, who presents a research program that, ironically, never really started because Bothe /
Geiger and Compton / Simon 1925 demonstrated strict energy and momentum conservation in Compton scattering. The \"virtual\" field is still the right concept, only it is not the
classic electromagnetic field, but the quantized.]{.small}\
**Hendrik Kramers - *The law of dispersion and Bohr\'s theory of spectra* (Nature 113, 673 (1924)).**\ [.pdf](https://uni-tuebingen.de/fileadmin/Uni_Tuebingen/Fakultaeten/MathePhysik/Institute/IAP/Forschung/MOettel/Geburt_QM/kramers_nature_113_673_1924.pdf)
**Hendrik Kramers - *The quantum theory of dispersion* (Nature 114, 310 (1924)).** [.pdf](https://uni-tuebingen.de/fileadmin/Uni_Tuebingen/Fakultaeten/MathePhysik/Institute/IAP/Forschung/MOettel/Geburt_QM/kramers_nature_114_310_1924.pdf)\
[Kramers had probably guessed the right dispersion formula using the correspondence principle before the Bohr-Kramers slater work appeared. The new formula now contained absorption
terms (with positive ones Oscillator strengths) as well as emission storms (with negative oscillator strengths). The Nature Letters contain only a sketch of the derivation and a reply
to a Breit objection. The full Van Vleck (see below) and Kramers / Heisenberg later supplied the derivation.]{.small}\
**John van Vleck - *The absorption of radiation by multiply periodic orbits, and its relation to the correspondence principle and the Rayleigh-Jeans law* (Phys. Rev. 24, 330 [.pdf](https://uni-tuebingen.de/fileadmin/Uni_Tuebingen/Fakultaeten/MathePhysik/Institute/IAP/Forschung/MOettel/Geburt_QM/vanvleck_pr_24_330_1924.pdf)\
(1924)).**
[At that time, physical review was still an obscure provincial journal (\"one of the funny journals just like the Japanese \"- Uhlenbeck) and van Vleck a clever young theorist with
Harvard doctorate and now a place in Minneapolis that, typical of that time, was filled with teaching obligations. In the present work, van Vleck demonstrates by deriving the Kramers
formula, that he on the semiclassical quantization was the state of discussion of the Copenhagen clique. Ironically, he had to in the following months work on a longer overview
article on \"old\" quantum theory, which became obsolete as soon as he appeared.A nice summary of the repetition and development of quantum mechanics in the USA gave Duncan and
Janssen ([.pdf
(1)](https://uni-tuebingen.de/fileadmin/Uni_Tuebingen/Fakultaeten/MathePhysik/Institute/IAP/Forschung/MOettel/Geburt_QM/V1_Duncan-Janssen_2007_Umdeutung-VanVleck_01.pdf), [.pdf
(2)](https://uni-tuebingen.de/fileadmin/Uni_Tuebingen/Fakultaeten/MathePhysik/Institute/IAP/Forschung/MOettel/Geburt_QM/V1_Duncan-Janssen_2007_Umdeutung-VanVleck_02.pdf)).]{.small}\
[1925/26 - Werner Heisenberg - About quantum mechanical reinterpretation of kinematic and mechanical relationships (Z. Phys. 33, 879 (1925)). .pdf
breakthrough]{#durchbruch}
[Heisenberg basically wanted to think again after great difficulties in the semiclassical quantization of helium and on the other hand the dispersion theory did not quite agree with
him agreed. It seemed unnatural to him that the classic orbit curve of the electron was still needed, although their properties did not appear evident in the radiation. A new quantum
mechanics should in his opinion only use transitional properties as kinematic variables, i.e. the Energy or frequency differences *ν (n, n-α)* of railways as well as transition
amplitudes in the Fourier laying of the railways *A (n, n-α)* (in today\'s language ⟨ n-α \| *x京* \|n ⟩). For the *A (n, n-α)* postulated Heisenberg matrix calculation rules without
the term \"matrix\" itself to use. The new quantum mechanics now consisted of\
1. Solve the classic equation of motion *d^2nd^x / dt^2nd^ + f (x) = 0* with matrix-valued position variables *x~nm~* .\
2nd The quantization condition is the Thomas Kuhn sum rule\
*h = 4πm Σ~α~(\| A (n, n + α) \|^2nd^ ω (n, n + α) - \|A (n, n-α) \|^2nd^ ω (n, n-α))* .\
The appearance of the Thomas Kuhn sum rule can only be understood in the context of the previous dispersion theory who can derive them. Heisenberg rewritten Bohr\'s quantization
condition and one Form sought that only contains transition amplitudes and should also be known and \"evident\". Since the hydrogen atom was too difficult in this form, Heisenberg
preferred the equation for the anisotropic to solve one-dimensional oscillator in fault theory. After being there in second fault regulations Having found energy conservation, he was
convinced that he was on the right track. This successful calculation for energy conservation was probably his famous and almost mystified today \"Helgoland experience\".]{.small}\
**Max Born and Pascual Jordan - *For quantum mechanics* (Z. Phys. 34, 858 (1925)).** [.pdf](https://uni-tuebingen.de/fileadmin/Uni_Tuebingen/Fakultaeten/MathePhysik/Institute/IAP/Forschung/MOettel/Geburt_QM/born_jordan_ZPhys_34_858_1925.pdf)\
[]{.small}\
**Paul Dirac - *The fundamental equations of quantum mechanics* (Proc. Royal Soc. A 109, 642 (1926)).** [.pdf](https://uni-tuebingen.de/fileadmin/Uni_Tuebingen/Fakultaeten/MathePhysik/Institute/IAP/Forschung/MOettel/Geburt_QM/dirac_ProcRoySocA_109_642_1926.pdf)\
[]{.small}\
**Max Born, Werner Heisenberg and Pascual Jordan - *For quantum mechanics.II* (Z. Phys. 35, 557 (1926)).** [.pdf](https://uni-tuebingen.de/fileadmin/Uni_Tuebingen/Fakultaeten/MathePhysik/Institute/IAP/Forschung/MOettel/Geburt_QM/born_jordan_heisenberg_ZPhys_35_557_1926.pdf)\
[This is the famous \"three-man work\" (it was not so common in those times that three Theorists stood together on a work \...).]{.small}\
[1924-26 - wave Louis de Broglie - Studies on quantum theory (Dissertation, Annales de Physique 3, 22 (1925)). .pdf
mechanics]{#wellen}
[De Broglie\'s dissertation introduces the idea of a wave-particle duality. Interestingly, de Broglie on this assumption thanks to the Lorentz transformations of special relativity
and the generalized relativistic dynmaic for a point particle. New quantum mechanical equations he could not win yet, but the Bohr quantization condition is now equivalent a resoance
condition for material waves.]{.small}\
**Erwin Schrödinger - *Quantization as a problem of intrinsic value. I-IV.*\ [.pdf (I)](https://uni-tuebingen.de/fileadmin/Uni_Tuebingen/Fakultaeten/MathePhysik/Institute/IAP/Forschung/MOettel/Geburt_QM/schrodinger_AnnPhys_384_361_1926.pdf) [.pdf
(Ann. Phys. 384, 361 (1926)).\ (II)](https://uni-tuebingen.de/fileadmin/Uni_Tuebingen/Fakultaeten/MathePhysik/Institute/IAP/Forschung/MOettel/Geburt_QM/schrodinger_AnnPhys_384_489_1926.pdf) [.pdf
(Ann. Phys. 384, 489 (1926)).\ (III)](https://uni-tuebingen.de/fileadmin/Uni_Tuebingen/Fakultaeten/MathePhysik/Institute/IAP/Forschung/MOettel/Geburt_QM/schrodinger_AnnPhys_385_437_1926.pdf) [.pdf
(Ann. Phys. 385, 437 (1926)).\ (IV)](https://uni-tuebingen.de/fileadmin/Uni_Tuebingen/Fakultaeten/MathePhysik/Institute/IAP/Forschung/MOettel/Geburt_QM/schrodinger_AnnPhys_386_109_1926.pdf)\
(Ann. Phys. 386, 109 (1926)).**
[]{.small}\
**Erwin Schrödinger - *About the relationship between Heisenberg-Born-Jordans quantum mechanics and mine* (Ann. Phys. 384, 734 (1926)).** [.pdf](https://uni-tuebingen.de/fileadmin/Uni_Tuebingen/Fakultaeten/MathePhysik/Institute/IAP/Forschung/MOettel/Geburt_QM/schrodinger_AnnPhys_384_734_1926.pdf)\
[]{.small}\
:::: goog-te-spinner-pos
::: goog-te-spinner-animation
{.goog-te-spinner}
:::
::::