Erwin Schrödinger

How to use this course

Every chemistry and physics student meets Schrödinger’s equation. Fewer know that it appeared in six months of 1926, written by a 38-year-old professor in Zürich who had so far worked on statistical physics, colour vision and radioactivity. Fewer still know that nine years later the same man named entanglement, or that his lectures on the physics of heredity helped draw a generation of physicists into biology. This course covers all three, along with a life spent moving between Vienna, Zürich, Berlin, Oxford, Graz and Dublin.

Each technical lesson begins with a paragraph for the general reader, then states results precisely, sketches derivations in modern notation, and ends with exercises whose solutions are folded. Schrödinger wrote \(K\) for \(h/2\pi\); we use \(\hbar\) throughout. Readers who want only the story can read Parts I and III and the opening paragraph of each lesson in Part II.

Timeline

Vienna, 1887–1910

Erwin Schrödinger was born on 12 August 1887 in Erdberg, a district of Vienna. His father Rudolf ran a small linoleum factory he had inherited, and was a serious amateur botanist. His mother Georgine, known as Emily, was the daughter of the chemist Alexander Bauer; her mother was English, from Leamington Spa. Erwin grew up bilingual in German and English in a comfortable house full of books.

A private tutor taught him at home until he was about ten. In the autumn of 1898 he entered the Akademisches Gymnasium, a classical school where Latin and Greek took as much time as mathematics. He was top of his class in almost every subject and kept a lifelong love of Greek philosophy and of poetry. He also read Schopenhauer, which led him later to the Upanishads and the Vedanta, sources that shaped his view of mind and self.

The university

In 1906 he entered the University of Vienna. Ludwig Boltzmann, whose statistical mechanics Schrödinger revered, killed himself in September 1906, before Schrödinger could attend his lectures. Boltzmann’s successor Friedrich Hasenöhrl gave a four-year cycle of lectures on theoretical physics, from analytical mechanics through Maxwell’s theory to statistical mechanics, and Schrödinger later called him the strongest influence of his student years. He also studied mathematics with Franz Mertens and Wilhelm Wirtinger. His doctoral thesis, defended on 20 May 1910, was experimental: a study of electrical conduction on the surface of insulators in moist air.

Exner’s institute and the war, 1910–1920

After a year of voluntary military service in the fortress artillery, Schrödinger became an assistant in Franz Exner’s physics institute in Vienna. He ran the laboratory course for students and wrote papers on a wide range of subjects: dielectrics, magnetism, atmospheric radioactivity, the kinetic theory of solids and the dynamics of crystal lattices. Exner’s circle cared about the foundations of probability and the place of chance in physical law, a theme that runs through Schrödinger’s whole career. He received his habilitation, the right to lecture, in 1914.

The First World War began weeks later. Schrödinger served as an artillery officer, mostly on the Italian front, and was cited for commanding a battery under fire. He kept reading and writing. He studied Albert Einstein’s general theory of relativity soon after it appeared, and in 1917 he was recalled to Vienna to teach meteorology. That year he published his first papers on quantum theory.

Colour

After the war, the collapse of Austria-Hungary left Viennese academics poor. Schrödinger worked on the physiology of colour. His 1920 papers on colour metrics treated the space of perceived colours as a three-dimensional manifold and asked what metric on it measures just-noticeable differences, a geometric approach to perception that remained influential. In 1919 he became engaged to Annemarie (Anny) Bertel. Because an associate professorship in Vienna paid too little to support a family, he looked abroad.

Wandering years and Zürich, 1920–1925

In 1920 Schrödinger married Anny and moved through three posts in eighteen months: assistant to Max Wien at Jena, extraordinary professor at the Technische Hochschule in Stuttgart, and full professor at Breslau. In late 1921 he accepted the chair of theoretical physics at the University of Zürich, where Einstein had taught in 1909–1911. He stayed six years.

He arrived exhausted and ill. Tuberculosis, diagnosed in this period, sent him to the Alpine resort of Arosa several times in the 1920s. In Zürich his closest colleague was the mathematician Hermann Weyl at the ETH, from whom he learned the mathematics of eigenvalue problems that would soon prove decisive. In 1922 he observed that if Weyl’s gauge factor is carried around a quantized Bohr orbit, its exponent becomes a whole-number multiple of a universal constant, a hint, in retrospect, that quantum conditions concern waves.

His research until 1925 was mostly in statistical physics: specific heats, the statistics of ideal gases and Einstein’s new Bose–Einstein statistics. Through Einstein’s 1925 papers he learned of Louis de Broglie’s 1924 thesis, which assigned a wave to every particle. In the autumn of 1925 Peter Debye, who led the joint physics colloquium of the University and the ETH, asked him to present de Broglie’s ideas. Debye remarked afterwards that a wave ought to obey a wave equation. Schrödinger went to Arosa for the Christmas holidays, and on 27 December 1925 he wrote to Wilhelm Wien that he hoped to have a vibrating system whose frequencies give the hydrogen levels.

From de Broglie waves to a wave equation

For the general reader. In the 1600s light was a puzzle: did it travel as particles along rays, or as waves? Hamilton showed in the 1830s that the mathematics of rays and the mathematics of particle orbits are the same. Schrödinger took this old analogy seriously. If ordinary mechanics is the “ray optics” of some hidden wave, then atoms, which are as small as the wavelength, need the full wave theory.

de Broglie’s relations

Einstein had attached to light quanta an energy and a momentum, \(E=h\nu\) and \(p=h/\lambda\). In 1924 de Broglie proposed the same relations for electrons and every other particle. A Bohr orbit is then allowed when a whole number of wavelengths fits around it, \(2\pi r=n\lambda\), which with \(p=h/\lambda\) gives Bohr’s condition \(pr=n\hbar\).

Hamilton–Jacobi as geometrical optics

For a particle of energy \(E\) in a potential \(V\), the time-independent Hamilton–Jacobi equation for Hamilton’s characteristic function \(W(\mathbf x)\) is

Surfaces \(W=\text{const}\) are like wavefronts, and particle trajectories are their normals, since \(\mathbf p=\nabla W\). In optics, wavefronts of a wave \(e^{ik_0 S}\) in a medium of refractive index \(n(\mathbf x)\) satisfy the eikonal equation \(|\nabla S|^2=n^2\), the short-wavelength limit of the Helmholtz equation \(\nabla^2\psi+k_0^2n^2\psi=0\). The two equations match if the local wavenumber is \(k=|\nabla W|/\hbar=\sqrt{2m(E-V)}/\hbar\), which is exactly de Broglie’s \(p=\hbar k\).

Conversely, writing \(\psi=A\,e^{iW/\hbar}\) and expanding in powers of \(\hbar\), the leading order reproduces the Hamilton–Jacobi equation. This is the WKB approximation, and it shows that classical mechanics is to wave mechanics as ray optics is to wave optics.

In his first paper Schrödinger presented the equation differently. He substituted \(W=\hbar\ln\psi\) into the Hamilton–Jacobi equation and, instead of solving it, required the integral of the resulting quadratic form to be stationary. The Euler–Lagrange equation of that variational problem is the equation above. In his second paper he gave the optical argument.

The relativistic equation came first

Schrödinger first tried the relativistic relation \((E-V)^2=p^2c^2+m^2c^4\), which leads to what is now called the Klein–Gordon equation. For hydrogen it gives fine-structure levels that disagree with Arnold Sommerfeld’s formula and with experiment, because it ignores electron spin. He set it aside and published the nonrelativistic limit, which gave the right gross structure.

Quantization as an eigenvalue problem

For the general reader. A violin string can vibrate only at certain pitches, because its ends are fixed. Schrödinger’s insight was that an atom is the same: its electron wave must fit around the nucleus and fade away at a distance, and this allows only certain frequencies. The rules for which energies are allowed, which Bohr had simply postulated, came out of the mathematics of standing waves.

The first paper, Quantisierung als Eigenwertproblem (Erste Mitteilung), was received by the Annalen der Physik on 27 January 1926. Its programme is stated in the title: integer quantum numbers arise as naturally as the number of nodes of a vibrating string.

Separation of variables

For the Coulomb potential \(V=-e^2/(4\pi\varepsilon_0 r)\), write \(\psi=R(r)\,Y_l^m(\theta,\varphi)\). The spherical harmonics satisfy \(L^2Y_l^m=\hbar^2l(l+1)Y_l^m\) and \(L_zY_l^m=\hbar mY_l^m\), with \(l=0,1,2,\dots\) and \(|m|\le l\). Single-valuedness in \(\varphi\) forces integer \(m\); regularity at the poles forces integer \(l\). With \(u(r)=rR(r)\) the radial equation becomes

Derivation sketch

Put \(\rho=r/a_0\) and \(E=-\hbar^2\kappa^2/(2m_e a_0^2)\). The equation becomes \(u''=\big[\kappa^2-\frac{2}{\rho}+\frac{l(l+1)}{\rho^2}\big]u\). Near \(\rho=0\), \(u\sim\rho^{l+1}\); for large \(\rho\), \(u\sim e^{-\kappa\rho}\). Writing \(u=\rho^{l+1}e^{-\kappa\rho}f(\rho)\) gives

A power series \(f=\sum c_j\rho^j\) has \(c_{j+1}/c_j=2\big(\kappa(j+l+1)-1\big)/\big((j+1)(j+2l+2)\big)\). If it does not terminate, \(c_{j+1}/c_j\to2\kappa/j\) and \(f\) grows like \(e^{2\kappa\rho}\), ruining normalizability. So the series must stop at some \(j=n_r\), which requires \(\kappa=1/(n_r+l+1)=1/n\). The polynomials \(f\) are associated Laguerre polynomials. The ground state is

Schrödinger’s result reproduced Bohr’s levels without Bohr’s postulates. It also gave something Bohr could not: wave functions, from which transition intensities and, in Lesson 06, the Stark effect could be computed.

Oscillators, wave packets, perturbations

For the general reader. Within weeks Schrödinger solved the simplest vibrating systems, built a wave packet that swings back and forth like a classical pendulum without spreading, and invented a method for computing how an atom’s levels shift in an electric field. Each was a test the new theory had to pass, and each still opens every quantum mechanics course.

The harmonic oscillator

The half-integer appeared naturally, as Heisenberg had found months earlier by matrix methods. The zero-point energy \(\tfrac12\hbar\omega\) had been suggested by spectroscopy of molecules; now it was forced. The rigid rotor with moment of inertia \(I\) gives \(E_l=\hbar^2l(l+1)/2I\), in place of the old \(\hbar^2l^2/2I\), and fitted band spectra of diatomic molecules.

The non-spreading packet

In a short paper in Die Naturwissenschaften in 1926, Schrödinger superposed oscillator states with Poisson weights and showed that the result is a Gaussian packet whose centre follows the classical motion exactly and whose width never changes. In modern notation this is the coherent state

for real \(\alpha\) with \(x_0=\sqrt{2\hbar/m\omega}\,\alpha\). He hoped all particles would turn out to be such packets. For hydrogen they are not: generic packets spread, which became one argument against reading \(\psi\) as a material wave. Coherent states returned in 1963 in Roy Glauber’s quantum optics.

Perturbation theory

Write \(H=H_0+\lambda H_1\) and expand \(E=E^{(0)}+\lambda E^{(1)}+\cdots\), \(\psi=\psi^{(0)}+\lambda\psi^{(1)}+\cdots\). Collecting first-order terms and taking the inner product with \(\psi^{(0)}_n\) gives the result that Schrödinger adapted from Lord Rayleigh’s theory of vibrating strings:

For hydrogen in a field \(F\) along \(z\), \(H_1=eFz\). The \(n=2\) level is fourfold degenerate. The only non-zero matrix element is \(\langle 2s|z|2p_0\rangle=-3a_0\), so the level splits into \(E_2\pm3ea_0F\) and two unshifted states. This linear Stark effect agreed with the measurements, and with the old quantum theory’s result, while giving intensities as well.

Time, equivalence and interpretation

For the general reader. In 1926 physics had two quantum theories that looked nothing alike. Heisenberg’s used tables of numbers that do not commute; Schrödinger’s used waves. Schrödinger proved they give the same predictions. He also wrote down how the wave changes in time. What the wave actually is remained in dispute, and Schrödinger lost that argument to Max Born.

The time-dependent equation

The first three communications dealt with fixed energies. In the fourth, received in June 1926, Schrödinger eliminated \(E\) by writing \(\psi\propto e^{-iEt/\hbar}\), and obtained

He accepted that \(\psi\) must be complex, a step he had resisted. He also extended the theory to time-dependent perturbations and derived the dispersion of light by atoms.

Equivalence

In Über das Verhältnis der Heisenberg–Born–Jordanschen Quantenmechanik zu der meinen (1926), Schrödinger showed how to build Heisenberg’s matrices from his waves. Choose an orthonormal basis of eigenfunctions \(\psi_k\) of \(H\), and replace each classical quantity \(F(q,p)\) by the operator \(\hat F=F(q,-i\hbar\,\partial/\partial q)\), suitably ordered. Then

The matrices so defined satisfy Heisenberg’s equations of motion, \(\dot F_{kl}=\frac{i}{\hbar}(E_k-E_l)F_{kl}\). Schrödinger’s argument showed that wave mechanics yields matrix mechanics. The converse, and the full statement that both are representations of the same abstract theory, came with Pauli’s unpublished letter, Carl Eckart’s paper, Paul Dirac and Pascual Jordan’s transformation theory, and finally John von Neumann’s Hilbert space formulation (1932). The Stone–von Neumann theorem later made precise in which sense the canonical commutation relations have only one representation.

What is ψ?

Schrödinger first read \(e|\psi|^2\) as a real, smeared-out charge density. Max Born, analysing collisions in the summer of 1926, proposed instead that \(|\psi|^2\) is a probability density for finding the particle. Born’s reading handles many particles, where \(\psi\) lives on configuration space \(\mathbb R^{3N}\) and cannot be a field in ordinary space. Schrödinger never accepted the probability view as complete, and his visit to Bohr in Copenhagen in October 1926 ended in exhausted disagreement.

Many electrons and the chemical bond

For the general reader. Schrödinger’s first paper derived his equation from a minimum principle. That principle turned out to be the most practical tool in the theory: it lets one estimate energies of atoms and molecules too complicated to solve exactly. In 1927, in Schrödinger’s Zürich, Walter Heitler and Fritz London used his wave mechanics to explain why two hydrogen atoms bind into a molecule. Chemistry became a branch of quantum physics.

The variational principle

For a discrete spectrum the proof is one line: expand \(\phi=\sum c_k\psi_k\), so \(E[\phi]=\sum|c_k|^2E_k/\sum|c_k|^2\ge E_0\). Stationarity follows by varying \(\phi^*\) with Lagrange multiplier \(E\) for the normalization. This is the form in which Schrödinger first wrote his equation in January 1926.

Configuration space

For \(N\) particles the wave function is a function \(\psi(\mathbf x_1,\dots,\mathbf x_N,t)\) on \(\mathbb R^{3N}\), and the Hamiltonian is \(\sum_i -\frac{\hbar^2}{2m_i}\nabla_i^2+V(\mathbf x_1,\dots,\mathbf x_N)\). Schrödinger stated this in 1926 and was troubled by it, because a wave on a \(3N\)-dimensional space cannot be a physical field in ordinary space. For identical electrons, Werner Heisenberg and Paul Dirac showed in 1926 that only wave functions antisymmetric under exchange of two electrons (including spin) occur, which is Pauli’s exclusion principle in wave language.

Heitler and London (1927)

For two protons \(A,B\) a distance \(R\) apart and two electrons, let \(a(\mathbf r)\), \(b(\mathbf r)\) be hydrogen 1s orbitals on each proton. Heitler and London used the trial functions

where \(S=\int ab\,d^3r\) is the overlap, \(J\) the classical Coulomb interaction of the two charge clouds, and \(K\) the exchange integral, which has no classical analogue. The symmetric spatial function \(\psi_+\) goes with the spin singlet. Because \(K\) is negative and large, \(E_+(R)\) has a minimum: the molecule binds. Their estimate gave a binding energy of about 3.1 eV at \(R\approx0.087\) nm, against the measured 4.75 eV at 0.074 nm. The triplet \(\psi_-\) is repulsive at all distances. The covalent bond is a consequence of exchange symmetry and the Coulomb force.

Entanglement and the cat

For the general reader. In 1935 Einstein, Boris Podolsky and Nathan Rosen argued that quantum mechanics is incomplete. Schrödinger, in correspondence with Einstein, went further. He showed that two systems that have interacted can be described only jointly, and he gave this feature its name, Verschränkung, entanglement. To show how strange the theory becomes if applied to everyday objects, he imagined a cat whose life is tied to a single radioactive atom.

Composite systems

The state of two systems lies in the tensor product \(\mathcal H_A\otimes\mathcal H_B\). A pure state is a product if it equals \(|a\rangle\otimes|b\rangle\), and entangled otherwise. In his paper in the Proceedings of the Cambridge Philosophical Society (1935), Schrödinger called entanglement “the characteristic trait of quantum mechanics”, the one that enforces its departure from classical thought.

The proof is the singular value decomposition of the coefficient matrix \(c_{jk}\) in \(|\Psi\rangle=\sum c_{jk}|j\rangle|k\rangle\). The entropy \(S=-\sum p_i\log p_i\) measures the entanglement.

Schrödinger found it disturbing that one party can “steer” the other into any of these ensembles at will. The result was rediscovered by Hughston, Jozsa and Wootters in 1993, and steering is now a resource studied in quantum information alongside entanglement and Bell nonlocality.

The cat

In Die gegenwärtige Situation in der Quantenmechanik, published in three parts in Die Naturwissenschaften in late 1935, Schrödinger described a cat sealed in a steel chamber with a tiny amount of radioactive material, a Geiger counter and a flask of poison. If an atom decays within the hour, the counter releases a hammer that breaks the flask. If the whole system is described by a wave function, then after an hour the wave function contains the living and the dead cat mixed in equal parts. He offered this as a reductio: a superposition that is acceptable for an atom becomes absurd when entanglement carries it up to a macroscopic object. The question of where and how definite outcomes arise, the measurement problem, is still debated. Decoherence theory explains why such superpositions are unobservable in practice; it does not by itself select one outcome.

Zitterbewegung and What Is Life?

For the general reader. Two of Schrödinger’s later ideas reached far beyond their starting points. In 1930 he found that the free electron of Dirac’s theory trembles at an enormous frequency. In 1943 he asked, as a physicist, how a few thousand atoms in a chromosome can carry hereditary information stably for generations, and guessed that the answer is a code written in an “aperiodic crystal”.

Zitterbewegung (1930)

For the Dirac Hamiltonian \(H=c\,\boldsymbol\alpha\cdot\mathbf p+\beta mc^2\), the velocity operator is \(\dot{\mathbf x}=\frac{i}{\hbar}[H,\mathbf x]=c\boldsymbol\alpha\), whose eigenvalues are \(\pm c\). Schrödinger solved the Heisenberg equations exactly for a free electron.

The oscillating term comes from interference between positive- and negative-energy components. For a packet built only from positive energies it disappears, which is how the effect is understood today. Analogues have been observed in trapped ions and other simulated Dirac systems.

The physics of heredity

In February 1943 Schrödinger lectured at Trinity College Dublin on the physical basis of life; the book What Is Life? appeared in 1944. He drew on the 1935 paper of Nikolai Timoféeff-Ressovsky, Karl Zimmer and Max Delbrück, which modelled the gene as a molecule. His argument has three steps.

1. The \(\sqrt n\) law. Statistical laws of physics are reliable because fluctuations in a system of \(n\) molecules are of relative size \(1/\sqrt n\). A gene, estimated to contain only about a thousand atoms or fewer, is too small to be governed by averages.
2. Stability from quantum mechanics. Its permanence must therefore come from quantum discreteness: a molecule sits in a deep energy minimum, and changes require crossing a barrier \(W\). The expected waiting time is \(t=\tau\,e^{W/kT}\), with \(\tau\) a molecular vibration period. A modest \(W\) gives lifetimes of thousands of years; a mutation is a rare quantum jump.
3. Order from order. An organism stays far from equilibrium by drawing order from its environment, feeding on “negative entropy”. The gene is an aperiodic crystal whose arrangement is a code script for development.

The book was read by many who moved from physics into biology. Francis Crick and James Watson both cited it as an early influence. The double helix (1953) vindicated the idea of a molecular code, though Schrödinger’s suggestion that life might require new physical laws did not prove necessary.

Berlin, Oxford, Graz, Dublin, 1927–1955

In 1927 Schrödinger succeeded Max Planck in the chair of theoretical physics at the University of Berlin. Berlin was then the centre of physics in Germany: Planck, Einstein, Max von Laue and Lise Meitner were his colleagues, and in 1929 he was elected to the Prussian Academy of Sciences. He attended the Fifth Solvay Conference in Brussels in October 1927, where the Copenhagen interpretation was set out and contested.

When the Nazis took power in 1933, Schrödinger, who was not Jewish, was under no direct threat. He left anyway, in protest at the dismissal of Jewish colleagues. Frederick Lindemann arranged a fellowship at Magdalen College, Oxford. Shortly after he arrived, in November 1933, he learned that he would share the Nobel Prize in Physics with Paul Dirac. Oxford was not a comfortable fit. Schrödinger lived openly with both his wife and Hilde March, the wife of his friend and assistant Arthur March, who bore his daughter in 1934. This arrangement, along with his dislike of college life, also weighed against a permanent offer from Princeton in 1934.

Graz and flight

In 1936, homesick, he accepted a chair at Graz. Two years later Germany annexed Austria. In March 1938 Schrödinger published a declaration of loyalty to the new regime in a Graz newspaper. He later regretted it publicly and privately. It did not help: in August 1938 he was dismissed as politically unreliable, having left Germany in 1933. He and Anny left Austria with almost nothing, travelling by way of Italy. After a short period in Oxford and a visiting post at Ghent, he moved to Dublin in 1939.

Dublin

The Irish prime minister Éamon de Valera, who had trained in mathematics, founded the Dublin Institute for Advanced Studies in 1940 with Schrödinger as director of its School of Theoretical Physics. He stayed sixteen years and worked on unified field theories in the style of Einstein’s, on the foundations of statistical thermodynamics, and on the expanding universe. His public lectures there produced What Is Life? (1944), Nature and the Greeks (1954) and Mind and Matter (1958). He was elected a Foreign Member of the Royal Society in 1949.

Return, death and legacy, 1956–1961

Schrödinger retired from Dublin in 1955 and returned to Vienna in 1956 as a professor emeritus at the university. Austria received him with honours: he was the first recipient of the Austrian Academy of Sciences’ new Erwin Schrödinger Prize and received the Pour le Mérite for Sciences and Arts in 1956. His health, damaged by recurring tuberculosis, declined. He died in Vienna on 4 January 1961, aged 73, and was buried in the Tyrolean village of Alpbach, where he had spent long holidays. His grave carries his equation.

Personal conduct

Schrödinger’s diaries, described by his biographer Walter Moore in 1989, record sexual relationships with several women and with teenage girls, including a fourteen-year-old girl he was tutoring in Vienna. In 2021 an article in the Irish Times described this conduct as abuse. In 2022 Trinity College Dublin announced that it would rename the lecture theatre that bore his name. Any honest account of the man includes this record alongside the physics.

Legacy

• Wave mechanics: the Schrödinger equation is the working tool of atomic, molecular, solid-state and chemical physics. Quantum chemistry is largely the art of solving it.
• Foundations: entanglement, steering and the cat define the questions that quantum information science and the measurement problem still address.
• Biology: What Is Life? helped bring physicists into molecular biology and popularized the idea of a genetic code.
• Honours: Nobel Prize in Physics (1933, with Dirac); Matteucci Medal (1927); Max Planck Medal (1937); member of the Pontifical Academy of Sciences (1936). The Erwin Schrödinger International Institute for Mathematical Physics in Vienna (1992), a lunar crater and the Austrian 1000-schilling note (1983–97) bear his name or face.

Connections

People linked to Erwin Schrödinger across this collection. A name without a link has no page here yet. See Erwin Schrödinger in the network of all 337 lives →

Teachers and advisors

• Franz Exner
• Friedrich Hasenöhrl 1906-1910

Students

• Fritz London
• Walter Heitler

Influenced by

• Carl Gustav Jacob Jacobi
• Louis de Broglie 1925
• Ludwig Boltzmann
• William Rowan Hamilton

Colleagues and collaborators

• Albert Einstein 1925-1955
• Hermann Weyl 1921-1927
• Max Born
• Max Planck 1926-1933
• Paul Dirac
• Peter Debye 1925
• Wolfgang Pauli
• Arthur March

Rivals

• Max Born
• Niels Bohr 1926
• Werner Heisenberg

Friends

• Hermann Weyl 1921-1927

Also mentioned in this life

• Arthur Compton
• Charles-Augustin de Coulomb
• Paul Ehrenfest
• Leonhard Euler
• Joseph Fourier
• Hans Geiger
• Hermann von Helmholtz
• Charles Hermite
• David Hilbert
• Joseph-Louis Lagrange
• James Clerk Maxwell
• Lise Meitner
• Isaac Newton
• Siméon Denis Poisson
• Lord Rayleigh
• Arnold Sommerfeld
• Max von Laue
• John von Neumann
• Wilhelm Wien

Fields

• quantum mechanics 6 lives
• statistical physics 3 lives

On CoursesHub

• Quantum Mechanics

Sources and further reading

Biography

1. J. J. O’Connor and E. F. Robertson, Erwin Schrödinger, MacTutor History of Mathematics.
2. Erwin Schrödinger, Wikipedia (with extensive references).
3. Erwin Schrödinger, biographical, NobelPrize.org.
4. University of Vienna, Schrödinger 100: treasures from the archive (letters of 1926).
5. W. Moore, Schrödinger: Life and Thought, Cambridge University Press, 1989.
6. W. Heitler, Erwin Schrödinger 1887–1961, Biographical Memoirs of Fellows of the Royal Society 7 (1961) 221–228.

Physics

1. E. Schrödinger, Quantisierung als Eigenwertproblem I–IV, Annalen der Physik 79 (1926) 361 and 489; 80 (1926) 437; 81 (1926) 109.
2. E. Schrödinger, Über das Verhältnis der Heisenberg–Born–Jordanschen Quantenmechanik zu der meinen, Annalen der Physik 79 (1926) 734–756.
3. E. Schrödinger, Der stetige Übergang von der Mikro- zur Makromechanik, Die Naturwissenschaften 14 (1926) 664–666.
4. E. Schrödinger, An undulatory theory of the mechanics of atoms and molecules, Physical Review 28 (1926) 1049–1070.
5. E. Schrödinger, Über die kräftefreie Bewegung in der relativistischen Quantenmechanik, Sitzungsberichte der Preussischen Akademie der Wissenschaften (1930).
6. E. Schrödinger, Die gegenwärtige Situation in der Quantenmechanik, Die Naturwissenschaften 23 (1935) 807–812, 823–828, 844–849.
7. E. Schrödinger, Discussion of probability relations between separated systems, Proc. Cambridge Phil. Soc. 31 (1935) 555–563; and Probability relations between separated systems, 32 (1936) 446–452.
8. E. Schrödinger, What Is Life? The Physical Aspect of the Living Cell, Cambridge University Press, 1944.
9. Schrödinger equation, Wikipedia (history section).
10. L. P. Hughston, R. Jozsa, W. K. Wootters, A complete classification of quantum ensembles having a given density matrix, Physics Letters A 183 (1993) 14–18.
11. M. Jammer, The Conceptual Development of Quantum Mechanics, McGraw-Hill, 1966.