Erwin Schrödinger developed the wave equation that serves as the foundation for all non-relativistic quantum mechanics. He shared the Nobel Prize for physics in 1933 with P. A. M. Dirac.

Schrödinger was born in Vienna on August 12th, 1887. Schrödinger's father Rudolf owned a linoleum business, his passions were botany and painting.

Schrödinger was an only child. He did not enter school until age eleven, instead learning at home from his parents, from a tutor, and from his aunts, one of whom taught him to speak English. The family spent the year before he entered school in England, where his mother had relatives.

At age eleven, Schrödinger enrolled in a Vienna Gymnasium that emphasized Latin and Greek. According to his biography on the Nobel Prize web site:

[He] appreciated the severe logic of ancient grammar and the beauty of German poetry. (What he abhorred was memorizing of data and learning from books.)^{1}

In 1906 he entered the University of Vienna, where Fritz Hasenöhrl had taken over as director of the physics department after Ludwig Boltzmann's suicide.

Schrödinger served in the Austro-Hungarian Empires' Fortress Artillery during World War I, and received a citation for leading troops in battle against Italian forces in 1915. In 1917 he was pulled off the front and reassigned to teach a course in meteorology to antiaircraft gunnery officers.

During the war he learned of Einstein's theory of general relativity (published in 1915) and wrote two papers on the subject. One paper presented a universe with no mass but with tension (anticipating, in some respects the modern theory of quintessence.) The other paper dealt with the issue of whether or not energy is conserved in general relativity, an issue that is still active and controversial.

Schrödinger's mentor, Hasenöhrl, did not survive the war.

After the war ended Schrödinger's mother was diagnosed with breast cancer. In 1919 his father died, in 1920 the family's savings were destroyed by inflation, in 1921 his mother died.

Amidst this turmoil, Schrödinger wed Annemarie Bertel, known as Anny. The two had a childless and famously unfaithful marriage, but remained married until Schrödinger's death in 1961.

[Anny and Erwin on their wedding day.]

Schrödinger taught at the University of Zürich from 1921 until 1927. During this time, in 1926, while having an affair with a lover who has never been identified, he developed the equation for which he won the Nobel Prize.

In 1925, Louis de Broglie published his PhD dissertation, in which he suggested that particles of matter, like light, could be treated as waves. While he was able to relate momentum to frequency, but did not have an actual wave equation.

[Anny Schrödinger, seated between Sommerfeld and Debeye.]

According to Felix Bloch, Peter Debeye told Schrödinger that in order to treat matter as waves you needed to have a wave equation. Schrödinger set about to find one.

Schrödinger associated the energy, E, and momentum, p, of a particle with the operators:

(Where i is the square root of negative one, and the h with a line through it is Plank's constant divided by 2 pi.)

Substituting these relations into the classical equation for the total energy of a particle:

(where m is mass, and V is potential energy), gives:

This is the Schrödinger equation.

In fact, Schrödinger first tried to use the (special) relativistic formula for energy, and came up with what today is called the Klein-Gordon equation. But this equation did not give the right predictions for the spectrum of hydrogen, and so he started over.

(If the recently discovered Higgs particle turns out to truly be a scalar, then it will obey the Klein-Gordon equation.)

The Schrödinger equation fits the spectrum of hydrogen, and is the basis of all non-relativistic quantum mechanics.

The interpretation of what a solution to the Schrödinger equation actually is, and how it relates to experiment, turned out to a tricky business.

The interpretation that seems to fit best with experiment was provided by Born: the wave function integrated over any region of space is the probability that the particle is in that region.

Bohr, Pauli, and Heisenberg elaborated on Born's interpretation, and developed what became known as the ''Copenhagen'' interpretation.

Because the wave function provides a probability and not a certainty, quantum mechanics is non-deterministic. But there is a more serious issue: after a measurement, the probability that the particle will be in exactly the same state, if you measure it again immediately, becomes one. So a wave function which had filled all space with probability, collapses to a point. And this collapse is instantaneous, in violation of Einstein's universal ''speed limit.''

In detail, the Copenhagen interpretation says that a quantum system is in a linear superposition until you measure it, and then a measurement causes it to collapse into a particular component of that superposition. The pre-measurement superposition is is governed by the deterministic and unitary Schrödinger equation, but the process of measurement, by a classical system, kills off all the components that you don't see, and so the process of measurement is not deterministic and is not unitary. You need two completely different kinds of evolution in quantum mechanics: the deterministic Schrödinger evolution, and the non-deterministic Heisenberg collapse. And the collapse dynamics requires the intervention of a classical system, so this kind of evolution requires both quantum mechanics and classical mechanics.

Because of this, can you never have a quantum mechanical description of the entire universe, because you can't have a measurement without a classical system. Also, the act of measuring takes on an almost magical significance, and causes quantum mechanical systems to violate the very mathematical laws by which their evolution is determined in the absence of measurement.

Schrödinger thought that this was nonsense.

If one has to stick to this damned quantum jumping, then I regret having ever been involved in this thing.^{2}

In order to dramatically demonstrate what he felt was wrong with the Copenhagen interpretation, Schrödinger developed a thought experiment.

Put a cat (which is a classical system) in a box with a quantum system mechanical system governed by the Schrödinger equation: a radioactive atom that may or may not decay over a certain period of time. Set up a contraption so that if and only if the atom decays, poison is released and the cat dies. Seal the box. Before a scientist comes along and opens the box, performing a measurement, the atom is in a superposed state of having decayed and not having decayed, therefore the cat is in a superposed state of being alive and being dead.

So here we have a quantum superposition on a macroscopic scale, and clearly something is not right. Why can't this sort of thing happen? And why do we never see live and dead cats, or any macroscopic objects, in superposition?

If you argue that the cat himself is the observer then you still don't solve the problem, instead you have another thought experiment, this one developed by Eugene Wigner.

Wigner's friend (or Schrödinger's cat) is doing an experiment on a quantum system that is in a superposition until he—the friend--measures it, whereupon, it collapses. Now Wigner wants to know what his friend has measured. Together, his friend and the quantum system that his friend measured form a single system and it is in a superposed state until Wigner measures it.

You can even do away with Wigner's friend and Schrödinger's cat and you still have a problem. Put some radioactive element that may or may not decay and a two-slit experiment into a box. Set it up so that if the radioactive element decays, then the second slit is closed and the superposition of the electron going through both slits is destroyed. If the element doesn't decay, then the superposition is maintained. Seal the box.

Before the box is opened and a measurement is made, the two-slit experiment is in a superposed state of being in a superposed state and being in a determinate state.

Schrödinger hoped that perhaps it was possible to keep the deterministic part of quantum mechanics--the part of the theory governed by his equation--and get rid of the collapse part—what are called Heisenberg events.

This is really the origin of the what is usually called the "many worlds" interpretation of quantum mechanics (developed more fully by Everrett in the 1950s) The obvious—although bizarre--way to reconcile what Wigner's friend measures and what Wigner measures, is to suppose that all versions of Wigner's friend, one corresponding to each possible measurement, actually, in some sense, exist; the live cat and the dead cat are both real.

Schrödinger seemed comfortable with this view but knew that most quantum theorists were not:

The idea that they be not alternatives but *all* really happening simultaneously seems lunatic to him, just *impossible*. He thinks that if the laws of nature took *this* form for, let me say, a quarter of an hour, we should find our surroundings rapidly turning into a quagmire, or sort of featureless jelly or plasma, all contours becoming blurred, we ourselves probably becoming jellyfish. It is strange that he should believe this. For I understand he grants that unobserved nature does behave this way--namely according to the wave equation.^{2}

[1927 Solvay conference, featuring Einstein, Dirac and many others.]

In 1927, Schrödinger succeeded Max Plank at the University of Berlin, where Einstein was also on the faculty (although he taught no classes).

in 1933, Schrödinger and P. A. M. Dirac were jointly awarded the Nobel Prize in physics for their contributions to the development of quantum mechanics. Werner Heisenberg, while technically awarded the 1932 Prize in physics, was honored at the same ceremony.

Heisenberg and Dirac both brought their mothers. Schrödinger brought his wife, Anny, who was his friend Hermann Weyl's mistress. Schrödinger did not bring his own current mistress, Hilde March--the wife of another friend. March was pregnant with Schrödinger's child.

[Left to right: Heisenberg's mother, Annie Schrödinger, Dirac's mother, Dirac, Heisenberg, Schrödinger, in Stockholm to recieve the Nobel Prize.]

After Hitler came to power in 1933, Einstein left Berlin for Princeton. Schrödinger moved back to Austria, to the University of Granz, 1936. But Austria was invaded by Germany that same year and so Schrödinger fled to Dublin, where the Dublin Institute for Advanced Studies was created for him at University College. He lived in Ireland for seventeen years, then returned to Austria, where he died, in 1961.

In 1943 Schrödinger delivered a series of talks at the Dublin Institute for Advanced Studies, which addressed the role of information flow and thermodynamics in living systems. In 1944 these talks were published as the book 'What is Life?''

One issue Schrödinger addressed was a seeming paradox: living systems seem to become more ordered over time, whereas the second law of thermodynamics says that the entropy of the universe, which is sometimes interpreted as a measure of disorder, always increases.

This was five years before Shannon published his seminal paper on information theory, seven years before the soviet general Boris Belousov began investigating non-equilibrium chemistry (obtaining results that were rejected as ''impossible'' when he tried to publish them)^{3} a decade before Paul Glansdorff and Ilya Prigogine began publishing papers on non-equilibrium thermodynamics, and more than a decade before E. T. Jaynes published his papers on the relationship between information theory and statistical mechanics.

We now know that the apparent paradox of living systems seeming to become more ordered is a result of applying ideas from equilibrium thermodynamics to far-form-equilibrium systems. To paraphrase Ilya Prigogine (winner of the 1976 Nobel Prize for chemistry) in equilibrium entropy is a driver of disorder; far-from equilibrium entropy is a driver of order.

Schrödinger's lectures and book were perhaps the most important spur to this wide-ranging research.

**Quotes:**

*In an honest search for knowledge you quite often have to abide by ignorance for an indefinite period. Instead of filling a gap by guesswork, genuine science prefers to put up with it; and this, not so much from conscientious scruples about telling lies, as from the consideration that, however irksome the gap may be, its obliteration by a fake removes the urge to seek after a tenable answer. ^{4}*

*It is certainly not in general the case that by acquiring a good all-round scientific education you so completely satisfy the innate longing for a religious or philosophical stabilization, in the face of the vicissitudes of everyday life, as to feel quite happy without anything more. What does happen often is that science suffices to jeopardize popular religious convictions, but not to replace them by anything else. This produces the grotesque phenomenon of scientifically trained, highly competent minds with an unbelievably childlike--undeveloped or atrophied--philosophical outlook. ^{4}*

*Scepticism alone is a cheap and barren affair. Scepticism in a man who has come nearer to the truth than anyone before, and yet clearly recognizes the narrow limits of his own mental construction, is great and fruitful, and does not reduce but doubles the value of the discoveries. ^{4}*

*Nobel Laureate*

*Prof. Erwin Rudolf Josef Alexander Schrödinger*

*1921-27 Professor of Theoretical Physics at UZH*

[1] http://www.nobelprize.org/nobel_prizes/physics/laureates/1933/schrodinger-bio.html

[2] Barrett. F. A. (1999). *The Quantum Mechanics of Minds and Worlds*. Oxford University Press, Oxford.

[3] Piela, Lucjan (2007). *Ideas of Quantum Chemistry*. Elsevier, Amsterdam.

[4] Schrödinger, E., (1954). *Nature and the Greeks*. Cambridge University Press, Cambridge.

[5] Schrödinger, E., (1944). *What is Life?* Cambridge University Press, Cambridge.

[6] Moore, Walter (1989). *Schrödinger, Life and Thought*. Cambridge University Press, Cambridge.

[7] Gribbin, John (2013). *Erwin Schrödinger and the Quantum Revolution*. John Wiley and Sons, Hoboken.

[8] McQuarrie, D. A., (2008). *Quantum Chemistry (Second Edition)*. University Science Books.

[9] Heisenberg, Werner (1983). *Encounters with Einstein*. Princeton University Press, Princeton.

[10] Gamow, George (1966). *Thirty Years That Shook Physics*. Dover, New York.

[11] http://www.mpiwg-berlin.mpg.de/en/news/features/feature15

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**Today's Birthday in Science: P. A. M. Dirac**

### Additional Info

- Birthday Date: Tuesday, 12 August 2014