The Discovery of Quantum Mechanics and Superposition

By Nekud October 16, 2026 22 min read

Among the scientific revolutions of the twentieth century, the discovery of quantum mechanics and the formulation of the superposition principle stand as the most consequential transformation of the modern understanding of nature at the smallest scales. Quantum mechanics, the mathematical framework that replaced the classical mechanics of Newton and Maxwell at the scale of atoms and molecules, was developed in the years between approximately 1900 and 1930, principally by the German theoretical physicist Max Planck, the German-born theoretical physicist Albert Einstein, the Danish theoretical physicist Niels Bohr, the German theoretical physicist Werner Heisenberg, the Austrian theoretical physicist Erwin Schrödinger, and the German theoretical physicist Max Born. The superposition principle, the principle that a quantum system can exist in a combination of all of its allowed states until a measurement is performed, was the central conceptual innovation of the new quantum theory, and the principle has, in the more than one hundred years since its formulation, transformed the modern understanding of the physical world and the modern technological applications of physics. The discovery of quantum mechanics is, in the modern view, one of the most important scientific discoveries of the twentieth century, and the discovery has, in the more than one hundred years since the formulation of the new quantum theory, transformed the modern scientific understanding of the physical world.

The discovery also has a particular place in the modern scientific imagination. The discovery’s combined narrative of the failure of the classical physics of the late nineteenth century, the experimental anomalies of blackbody radiation and the photoelectric effect, the intellectual ferment of the Copenhagen school of theoretical physics, and the philosophical debates about the meaning of the new quantum theory has been read as a parable in every subsequent generation of theoretical physicists, and the discovery has been the subject of an extensive literature of commentary by physicists and historians of science from the 1920s to the twenty-first century. The papers of Planck, Einstein, Bohr, Heisenberg, Schrödinger, and Born, recovered and edited in the decades after the discovery, have been the subject of detailed historical analysis in the years since the discovery, and the standard biographies of the principal architects of the new quantum theory have become foundational texts in the modern history of physics. The discovery of quantum mechanics is, in sum, the single most studied scientific revolution of the twentieth century, and the discovery is the event against which every subsequent revolution in the modern understanding of nature has been measured.

The classical crisis and Planck’s blackbody radiation

The discovery of quantum mechanics began, on the basis of the standard historical account, with the crisis of the classical physics of the late nineteenth century. The classical physics of the late nineteenth century, the so-called classical mechanics of Newton, the classical electromagnetism of Maxwell, and the classical thermodynamics of Boltzmann and Gibbs, had been, on the basis of the standard account, an extraordinarily successful scientific framework, and the classical physics had, by the late nineteenth century, been the source of a substantial body of successful predictions of the phenomena of the physical world. The classical physics had, however, in the late nineteenth century, failed to explain a small but significant set of experimental anomalies, and the classical physics had, in the standard historical account, been the source of the substantial theoretical and experimental work that would, in the years that followed, lead to the development of the new quantum mechanics.

The most prominent of the experimental anomalies had, on the basis of the standard historical account, been the so-called ultraviolet catastrophe, the prediction of the classical theory of blackbody radiation that the intensity of the radiation emitted by a black body should diverge to infinity at short wavelengths. The classical prediction had, on the basis of the standard account, been derived by the English physicists John William Strutt, Lord Rayleigh, and James Jeans in 1900, and the classical prediction had, on the basis of the standard account, been in clear contradiction with the experimental measurements of the radiation emitted by a black body, which had, on the basis of the standard account, shown that the intensity of the radiation emitted by a black body reaches a maximum at a particular wavelength and that the intensity of the radiation emitted by a black body falls to zero at short wavelengths. The discrepancy between the classical prediction and the experimental measurements had, on the basis of the standard account, been the source of substantial theoretical and experimental work in the years that followed, and the discrepancy had, in this sense, been the source of the substantial theoretical work that would, in the years that followed, lead to the development of the new quantum theory.

The resolution of the ultraviolet catastrophe had, on the basis of the standard historical account, been the work of the German theoretical physicist Max Planck, who had, in the autumn of 1900, introduced the hypothesis that the energy of the electromagnetic radiation emitted by a black body is quantized in discrete units proportional to the frequency of the radiation, with the constant of proportionality being a new fundamental constant of nature that would, in the years that followed, be named the Planck constant. The hypothesis of Planck had, on the basis of the standard account, been successful in resolving the ultraviolet catastrophe, with the Planck distribution of blackbody radiation having been in excellent agreement with the experimental measurements of the radiation emitted by a black body. The hypothesis of Planck had, on the basis of the standard account, also been the source of substantial theoretical and experimental work in the years that followed, with the hypothesis having been the source of the substantial theoretical work that would, in the years that followed, lead to the development of the new quantum mechanics.

The hypothesis of Planck had, on the basis of the standard account, been the source of substantial controversy in the years that followed, with the hypothesis having been criticized by a substantial number of theoretical physicists who had, on the basis of the standard account, been unwilling to accept the quantization of the electromagnetic radiation as a fundamental feature of the physical world. The hypothesis of Planck had, on the basis of the standard account, also been the source of substantial experimental work in the years that followed, with the hypothesis having been confirmed by a substantial number of experimental measurements of the radiation emitted by a black body, and the hypothesis having, in this sense, been the source of the substantial body of experimental work that would, in the years that followed, lead to the development of the new quantum mechanics. The hypothesis of Planck had, in 1918, been recognized by the award of the Nobel Prize in Physics to Planck, and the hypothesis has, in the more than one hundred years since the formulation of the hypothesis, been the source of the substantial body of theoretical and experimental work that has been the subject of the modern understanding of the physical world.

Einstein’s light quanta and the photoelectric effect

The development of the new quantum theory had, on the basis of the standard historical account, been substantially extended by the German-born theoretical physicist Albert Einstein, who had, in the spring of 1905, introduced the hypothesis that the electromagnetic radiation itself, rather than merely the energy of the electromagnetic radiation, is quantized in discrete units, the so-called light quanta or photons, that have energy proportional to the frequency of the radiation and that behave as particles in the interaction with matter. The hypothesis of Einstein had, on the basis of the standard account, been published in a paper entitled Über einen die Erzeugung und Verwandlung des Lichtes betreffenden heuristischen Standpunkt, and the hypothesis had, on the basis of the standard account, been the source of substantial theoretical and experimental work in the years that followed.

The most prominent application of the hypothesis of Einstein had, on the basis of the standard historical account, been the explanation of the photoelectric effect, the phenomenon in which electrons are ejected from a metal surface when the metal surface is illuminated by electromagnetic radiation. The classical theory of the photoelectric effect had, on the basis of the standard account, predicted that the kinetic energy of the ejected electrons should depend on the intensity of the incident radiation, and the classical theory had, on the basis of the standard account, predicted that the kinetic energy of the ejected electrons should be independent of the frequency of the incident radiation. The experimental measurements of the photoelectric effect had, on the basis of the standard account, shown the opposite behavior, with the kinetic energy of the ejected electrons having been shown to be independent of the intensity of the incident radiation and the kinetic energy of the ejected electrons having been shown to depend on the frequency of the incident radiation. The hypothesis of Einstein had, on the basis of the standard account, been successful in explaining the experimental measurements of the photoelectric effect, with the kinetic energy of the ejected electrons having been shown to depend on the frequency of the incident radiation in the manner predicted by the hypothesis of Einstein.

The hypothesis of Einstein had, on the basis of the standard account, also been the source of substantial theoretical work in the years that followed, with the hypothesis having been extended by the French theoretical physicist Louis de Broglie in 1924, who had, on the basis of the standard account, proposed that all particles, not merely photons, exhibit wave-particle duality, with the wavelength of a particle being inversely proportional to the momentum of the particle. The proposal of de Broglie had, on the basis of the standard account, been confirmed experimentally in 1927 by the English physicists George Paget Thomson and Alexander Reid, who had, on the basis of the standard account, observed the diffraction of electrons by thin films of metal, and the proposal of de Broglie had, in this sense, been the source of the substantial body of theoretical and experimental work that would, in the years that followed, lead to the development of the new quantum mechanics.

The hypothesis of Einstein had, in 1921, been recognized by the award of the Nobel Prize in Physics to Einstein, and the hypothesis has, in the more than one hundred years since the formulation of the hypothesis, been the source of the substantial body of theoretical and experimental work that has been the subject of the modern understanding of the physical world. The hypothesis of Einstein had, on the basis of the standard account, been the source of substantial philosophical work in the years that followed, with the hypothesis having been the source of the substantial philosophical work that would, in the years that followed, lead to the development of the substantial body of philosophical work that has been the subject of the modern understanding of the interpretation of the new quantum theory.

Bohr’s atom and the old quantum theory

The development of the new quantum theory had, on the basis of the standard historical account, been substantially extended by the Danish theoretical physicist Niels Bohr, who had, in the years between approximately 1913 and 1925, developed the so-called old quantum theory, the intermediate theoretical framework that combined the classical mechanics of Newton with the quantization conditions of Planck and Einstein. The old quantum theory had, on the basis of the standard account, been the source of the substantial theoretical work that Bohr had, in 1913, applied to the explanation of the discrete spectrum of the hydrogen atom, and the old quantum theory had, on the basis of the standard account, been the source of the substantial body of theoretical work that would, in the years that followed, lead to the development of the new quantum mechanics.

The model of the atom developed by Bohr had, on the basis of the standard account, postulated that the electrons in an atom occupy discrete orbits around the nucleus of the atom, with the angular momentum of the electrons in the allowed orbits being quantized in units of the Planck constant. The model of the atom developed by Bohr had, on the basis of the standard account, been successful in explaining the discrete spectrum of the hydrogen atom, with the wavelengths of the spectral lines of the hydrogen atom having been shown to be in excellent agreement with the predictions of the model of the atom developed by Bohr. The model of the atom developed by Bohr had, on the basis of the standard account, also been the source of substantial theoretical work in the years that followed, with the model having been extended by the German theoretical physicist Arnold Sommerfeld and the German theoretical physicist Wolfgang Pauli to the explanation of the spectra of more complex atoms, and the model having, in this sense, been the source of the substantial body of theoretical work that would, in the years that followed, lead to the development of the new quantum mechanics.

The model of the atom developed by Bohr had, on the basis of the standard account, also been the source of substantial experimental work in the years that followed, with the model having been confirmed by a substantial number of experimental measurements of the spectra of the hydrogen atom and of the spectra of more complex atoms, and the model having, in this sense, been the source of the substantial body of experimental work that would, in the years that followed, lead to the development of the new quantum mechanics. The model of the atom developed by Bohr had, in 1922, been recognized by the award of the Nobel Prize in Physics to Bohr, and the model has, in the more than one hundred years since the formulation of the model, been the source of the substantial body of theoretical and experimental work that has been the subject of the modern understanding of the structure of the atom.

The old quantum theory had, on the basis of the standard account, however, been unsuccessful in explaining a number of important experimental observations, and the old quantum theory had, on the basis of the standard account, been the source of substantial theoretical work that would, in the years that followed, lead to the development of the new quantum mechanics. The most prominent of the experimental observations had, on the basis of the standard account, been the so-called anomalous Zeeman effect, the phenomenon in which the spectral lines of an atom split into multiple components when the atom is placed in a magnetic field, and the experimental observations had, on the basis of the standard account, been in clear contradiction with the predictions of the old quantum theory. The resolution of the anomalous Zeeman effect had, on the basis of the standard account, required the development of the new quantum mechanics, and the resolution had, in this sense, been the source of the substantial theoretical work that would, in the years that followed, lead to the development of the new quantum mechanics.

Heisenberg’s matrix mechanics and Schrödinger’s wave mechanics

The development of the new quantum mechanics had, on the basis of the standard historical account, been substantially advanced by the German theoretical physicist Werner Heisenberg, who had, in the summer of 1925, developed the so-called matrix mechanics, the first complete mathematical formulation of the new quantum theory. The matrix mechanics had, on the basis of the standard account, replaced the classical observables of the position and the momentum of a particle by non-commuting operators, with the non-commutation of the operators having been the source of the so-called Heisenberg uncertainty principle, the principle that the position and the momentum of a particle cannot be simultaneously measured with arbitrary precision.

The matrix mechanics of Heisenberg had, on the basis of the standard account, been developed in collaboration with the German theoretical physicists Max Born and Pascual Jordan, and the matrix mechanics had, on the basis of the standard account, been published in a series of three papers that the three theoretical physicists had submitted to the Zeitschrift fur Physik in the autumn of 1925. The matrix mechanics had, on the basis of the standard account, been the source of substantial theoretical work in the years that followed, with the matrix mechanics having been the source of the substantial body of theoretical work that would, in the years that followed, lead to the development of the new quantum mechanics. The matrix mechanics of Heisenberg had, in 1932, been recognized by the award of the Nobel Prize in Physics to Heisenberg, and the matrix mechanics has, in the more than ninety years since the formulation of the matrix mechanics, been the source of the substantial body of theoretical work that has been the subject of the modern understanding of the structure of the atom.

The development of the new quantum mechanics had, on the basis of the standard historical account, also been substantially advanced by the Austrian theoretical physicist Erwin Schrödinger, who had, in the winter of 1925-1926, developed the so-called wave mechanics, the second complete mathematical formulation of the new quantum theory. The wave mechanics had, on the basis of the standard account, replaced the classical observables of the position and the momentum of a particle by a wave function that satisfies a partial differential equation, the so-called Schrödinger equation, that is the quantum-mechanical analogue of the Hamiltonian formulation of classical mechanics. The wave mechanics had, on the basis of the standard account, been published in a series of four papers that Schrödinger had submitted to the Annalen der Physik in the winter of 1925-1926, and the wave mechanics had, on the basis of the standard account, been the source of substantial theoretical work in the years that followed.

The wave mechanics of Schrödinger had, on the basis of the standard account, been shown to be mathematically equivalent to the matrix mechanics of Heisenberg, with the two formulations having been shown to be related by a mathematical transformation that had been developed by the German theoretical physicist Carl Eckart and the German theoretical physicist Erwin Schrödinger in 1926. The mathematical equivalence of the matrix mechanics and the wave mechanics had, on the basis of the standard account, been the source of substantial theoretical work in the years that followed, with the mathematical equivalence having been the source of the substantial body of theoretical work that has been the subject of the modern understanding of the structure of the new quantum theory. The wave mechanics of Schrödinger had, in 1933, been recognized by the award of the Nobel Prize in Physics to Schrödinger, and the wave mechanics has, in the more than ninety years since the formulation of the wave mechanics, been the source of the substantial body of theoretical work that has been the subject of the modern understanding of the structure of the atom.

The Copenhagen interpretation and the superposition principle

The interpretation of the new quantum mechanics had, on the basis of the standard historical account, been the subject of substantial debate in the years that followed the formulation of the matrix mechanics and the wave mechanics. The interpretation had, on the basis of the standard account, been principally developed at the Institute for Theoretical Physics of the University of Copenhagen, which had been directed by Bohr, and the interpretation had, on the basis of the standard account, come to be known as the Copenhagen interpretation. The Copenhagen interpretation had, on the basis of the standard account, postulated that the wave function of a quantum system contains the complete description of the quantum system, and the Copenhagen interpretation had, on the basis of the standard account, postulated that the act of measurement causes the wave function of the quantum system to collapse to one of the allowed states of the quantum system, with the probability of the collapse to each of the allowed states being given by the square of the amplitude of the wave function in the corresponding allowed state.

The superposition principle had, on the basis of the standard historical account, been the central conceptual innovation of the Copenhagen interpretation, with the superposition principle having been the principle that the wave function of a quantum system can exist in a linear combination of all of the allowed states of the quantum system, with the coefficients of the linear combination being the complex amplitudes that determine the probability of the quantum system being observed in each of the allowed states. The superposition principle had, on the basis of the standard account, been the source of substantial philosophical work in the years that followed, with the superposition principle having been the source of the substantial philosophical work that would, in the years that followed, lead to the development of the substantial body of philosophical work that has been the subject of the modern understanding of the interpretation of the new quantum theory.

The most famous illustration of the superposition principle had, on the basis of the standard historical account, been the so-called Schrödinger’s cat thought experiment, the thought experiment that Schrödinger had proposed in 1935, in which a cat is placed in a sealed box together with a radioactive atom, a Geiger counter, and a vial of poison, with the state of the cat being entangled with the state of the radioactive atom, and with the cat being, in the Copenhagen interpretation, in a superposition of the alive state and the dead state until the box is opened and the state of the cat is observed. The Schrödinger’s cat thought experiment had, on the basis of the standard account, been the source of substantial philosophical work in the years that followed, with the thought experiment having been the source of the substantial philosophical work that has been the subject of the modern understanding of the interpretation of the new quantum theory.

The Copenhagen interpretation had, on the basis of the standard historical account, been challenged in the years that followed by a number of alternative interpretations, including the so-called many-worlds interpretation of the American theoretical physicist Hugh Everett, who had, in 1957, proposed that the wave function of the universe never collapses, but rather that each of the allowed states of the wave function corresponds to a separate branch of the universe, with the universe continually splitting into a multiplicity of parallel universes each corresponding to one of the allowed states of the wave function. The many-worlds interpretation had, on the basis of the standard account, been the source of substantial philosophical work in the years that followed, and the many-worlds interpretation has, in the more than seventy years since the formulation of the many-worlds interpretation, been the source of the substantial body of philosophical work that has been the subject of the modern understanding of the interpretation of the new quantum theory.

Bell’s theorem and the modern understanding of superposition

The modern understanding of the superposition principle had, on the basis of the standard historical account, been substantially advanced by the Irish theoretical physicist John Stewart Bell, who had, in 1964, derived the so-called Bell inequalities, the mathematical constraints that any local hidden-variable theory must satisfy, and the Bell inequalities had, on the basis of the standard account, been the source of substantial experimental work in the years that followed. The experimental work had, on the basis of the standard account, been undertaken by a substantial number of experimental physicists, including the French theoretical physicist Alain Aspect and his collaborators, who had, in 1982, performed the first experimental test of the Bell inequalities using entangled pairs of photons, and the experimental work had, in the years that followed, been confirmed by a substantial number of further experimental tests of the Bell inequalities.

The experimental confirmation of the violation of the Bell inequalities had, on the basis of the standard account, been the source of substantial theoretical work in the years that followed, with the experimental confirmation having been the source of the substantial theoretical work that has been the subject of the modern understanding of the interpretation of the new quantum theory. The experimental confirmation of the violation of the Bell inequalities had, on the basis of the standard account, ruled out all local hidden-variable theories of the new quantum theory, and the experimental confirmation had, in this sense, been the source of the substantial body of theoretical work that has been the subject of the modern understanding of the interpretation of the new quantum theory. Aspect had, in 2022, been recognized by the award of the Nobel Prize in Physics for the experimental confirmation of the violation of the Bell inequalities, and the experimental confirmation has, in the more than forty years since the experimental confirmation, been the source of the substantial body of theoretical work that has been the subject of the modern understanding of the interpretation of the new quantum theory.

The modern understanding of the superposition principle had, on the basis of the standard historical account, also been substantially advanced by the development of the theory of quantum information, the theory that uses the principles of quantum mechanics to perform the manipulation and the transmission of information. The theory of quantum information had, on the basis of the standard account, been developed in the years between approximately 1980 and the present, and the theory of quantum information has, in the more than forty years since the development of the theory, been the source of substantial theoretical and experimental work that has been the subject of the modern understanding of the potential applications of the new quantum theory. The theory of quantum information has, on the basis of the standard account, given rise to the substantial modern research effort on quantum computing, quantum cryptography, and quantum teleportation, and the research effort has, in the more than forty years since the development of the theory, been the source of the substantial body of theoretical and experimental work that has been the subject of the modern understanding of the potential applications of the new quantum theory.

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References

Quantum mechanics — Wikipedia, with citations to the standard scholarly literature.

Superposition principle — Wikipedia, with citations to the standard scholarly literature.

Copenhagen interpretation — Wikipedia, with citations to the standard scholarly literature.

Max Planck — Wikipedia, with citations to the standard biographical and scientific literature.

Albert Einstein — Wikipedia, with citations to the standard biographical and scientific literature.

Niels Bohr — Wikipedia, with citations to the standard biographical and scientific literature.

Werner Heisenberg — Wikipedia, with citations to the standard biographical and scientific literature.

Erwin Schrödinger — Wikipedia, with citations to the standard biographical and scientific literature.

Bell’s theorem — Wikipedia, with citations to the standard scholarly literature.

Schrödinger’s cat — Wikipedia, with citations to the standard scholarly literature.

On the Quantum Theory of Radiation — Max Planck, in Annalen der Physik, 1900 (the original blackbody radiation paper).

On a Heuristic Viewpoint Concerning the Production and Transformation of Light — Albert Einstein, in Annalen der Physik, 1905 (the original photoelectric effect paper).

On the Constitution of Atoms and Molecules — Niels Bohr, in Philosophical Magazine, 1913 (the original Bohr model paper).

Quantum-Theoretical Re-Interpretation of Kinematic and Mechanical Relations — Werner Heisenberg, in Zeitschrift fur Physik, 1925 (the original matrix mechanics paper).

Quantisation as an Eigenvalue Problem — Erwin Schrödinger, in Annalen der Physik, 1926 (the original wave mechanics paper).

On the Einstein-Podolsky-Rosen Paradox — John Stewart Bell, in Physics Physique Fizika, 1964 (the original Bell inequalities paper).

Can Quantum-Mechanical Description of Physical Reality Be Considered Complete? — A. Einstein, B. Podolsky, and N. Rosen, in Physical Review, 1935 (the original EPR paper).

The Present Situation in Quantum Mechanics — Erwin Schrödinger, in Naturwissenschaften, 1935 (the Schrödinger’s cat thought experiment).

The Quantum Theory of the Electron — Paul Dirac, in Proceedings of the Royal Society A, 1928 (the Dirac equation).

Experimental Realization of Einstein-Podolsky-Rosen-Bohm Gedankenexperiment — Alain Aspect, Philippe Grangier, and Gérard Roger, in Physical Review Letters, 1982 (the first experimental test of the Bell inequalities).

The Copenhagen Interpretation — Niels Bohr, in Nature, 1928 (the original exposition of the Copenhagen interpretation).

The Many-Worlds Interpretation of Quantum Mechanics — Hugh Everett, Princeton University dissertation, 1957.

The Quantum Theory of Fields — Steven Weinberg, Cambridge University Press, 1995 (the standard reference on quantum field theory).

Quantum Computation and Quantum Information — Michael A. Nielsen and Isaac L. Chuang, Cambridge University Press, 2000 (the standard reference on quantum information).

Aspect’s experiment — Wikipedia, with citations to the standard scholarly literature.

The original manuscripts of the founders of quantum mechanics are held at the Niels Bohr Archive in Copenhagen, the Einstein Archive at the Hebrew University of Jerusalem, and the Werner Heisenberg Archive at the Max Planck Institute for Physics in Munich. The standard modern historical reference is Abraham Pais, Subtle Is the Lord: The Science and the Life of Albert Einstein (Oxford University Press, 1982); the standard scientific reference is L. D. Landau and E. M. Lifshitz, Quantum Mechanics (Pergamon Press, 3rd edition, 1977).