Schrödinger,
Erwin

Schrödinger, Erwin (1887-1961), Austrian physicist and Nobel
laureate. Schrödinger formulated the theory of wave mechanics, which describes
the behavior of the tiny particles that make up matter
in terms of waves. Schrödinger formulated the Schrödinger wave equation to
describe the behavior of electrons (tiny, negatively
charged particles) in atoms. For this achievement, he was awarded the 1933
Nobel Prize in physics with British physicist Paul Dirac
and German physicist Werner Heisenberg, who also made important advances in the
theory of atomic structure. *See also *Quantum Theory; Atom.

Schrödinger was born in Vienna, Austria. His father was an
oilcloth manufacturer who had studied chemistry, and his mother was the
daughter of a chemistry professor. He attended an elementary school in
Innsbruck for a few weeks, but Schrödinger received most of his early education
from a private tutor. In 1898 he entered the Gymnasium in Vienna, where he studied
mathematics, physics, and ancient languages. He then attended the University of
Vienna from 1906 to 1910, specializing in physics. Schrödinger obtained his
doctoral degree in physics in 1910. After a year in military training, he
returned to the university to teach a first-year physics laboratory class. His
early research ranged over many topics in experimental and theoretical physics.

During World War I (1914-1918) Schrödinger served as an artillery
officer and then returned to his previous post at Vienna. Conditions were
difficult in Austria after the war, and in 1920 Schrödinger decided to go to
Germany. After a series of short-lived posts at the University of Jena,
Stuttgart University, and the University of Breslau (now Wrocław,
Poland) in 1920 and 1921, he became a professor of physics at the University of
Zürich in Switzerland in 1921.

Schrödinger's most important work was done at Zürich,
and his work received much attention. He succeeded German physicist Max Planck
as professor of theoretical physics at the University of Berlin in 1927.
Schrödinger remained there until the rise of the National Socialist (Nazi)
movement in 1933, when he went to the University of Oxford in England. There he
became a fellow of Magdalen College. Homesick, he
returned to Austria in 1936 to take up a post at Graz University, but the Nazi
takeover of Austria in 1938 placed Schrödinger in danger. Schrödinger was not
Jewish, but his opposition to Nazi policies made him a potential target. The
prime minister of Ireland, Eamon de Valera, helped Schrödinger get out of Austria. De Valera’s help also led to an appointment to a post at the
Institute for Advanced Studies in Dublin in 1939. Schrödinger continued work in
theoretical physics in Dublin until 1956, when he returned to Austria to a
chair at the University of Vienna. He stayed at the University of Vienna until
his death.

Schrödinger's great discovery of wave mechanics originated with
the work of French physicist Louis de Broglie. In
1923 de Broglie used ideas from German American
physicist Albert Eintstein’s special theory of
relativity to show that an electron, or any other particle, has a wave
associated with it (*see *Albert Einstein). De Broglie’s
work resulted in the equation λ = h/p, where λ is the wavelength of
the associated wave, *h* is a number called Planck's constant, and *p*
is the momentum of the particle. Physicists immediately deduced that if
particles (particularly electrons) have waves, then a particular type of
partial differential equation known as a *wave equation* should be able to
describe their behavior. These ideas were taken up by
both de Broglie and Schrödinger, and in 1926 each
published the same wave equation. Unfortunately, while the equation is true, it
was of very little help in explaining the behavior of
particles.

Later the same year Schrödinger used a new approach. He studied
the mathematics of partial differential equations and the Hamiltonian function,
a powerful idea in mechanics developed by British mathematician Sir William
Rowan Hamilton in the mid-1800s. Schrödinger formulated an equation in terms of
the energy of the electron and the energy of the electric field in which it was
situated. Partial differential equations have many solutions, but solutions to
Schrödinger’s equation had to meet strict conditions to be useful in describing
the electron. Among other things, they had to be finite and possess only one
value. These solutions were associated with special values of the electron’s
energy level, known as *proper values* or *eigenvalues**.*

Schrödinger solved the equation for the hydrogen atom, V = –e^{2}/r,
in which *V* is the energy of the electric field surrounding the electron,
*e* is the electron's charge, and *r* is its distance from the atom’s
nucleus. He found that the eigenvalues of the electron’s
energy corresponded with those of the energy levels given in the older theory
of Danish physicist Niels Bohr. Bohr’s theory of the
atom described electrons orbiting atoms in strict circular orbits at particular
distances that corresponded to specific levels of energy. In the hydrogen atom
(which consists of one electron and one proton), the wave function Schrödinger
derived instead describes where physicists are most likely to find the
electron. The electron is most likely to be where Bohr predicted it to be, but
it does not follow a strictly circular orbit. The electron is described by the
more complicated notion of an *orbital*—a region in space where the
electron has varying degrees of probability of being found.

Schrödinger's wave equation can describe atoms other than hydrogen
as well as molecules and ions (atoms or molecules with electric charge), but
such cases are very difficult to solve. In a few such cases physicists have
found approximate solutions, usually with a computer carrying out the numerical
work.

Schrödinger's mathematical description of electron waves found
immediate acceptance. The mathematical description matched what scientists had
learned about electrons by observing them and their effects. In 1925, a year
before Schrödinger published his results, German-British physicist Max Born and
German physicist Werner Heisenberg developed a mathematical system called
matrix mechanics. Matrix mechanics also succeeded in describing the structure
of the atom, but it was totally theoretical. It gave no picture of the atom
that physicists could verify observationally. Schrödinger's vindication of de Broglie's idea of electron waves immediately overturned
matrix mechanics, though later physicists showed that wave mechanics is
equivalent to matrix mechanics.

During his later years Schrödinger became increasingly worried by
the uncertain nature of quantum mechanics, of which wave mechanics is a part.
Schrödinger believed he had produced a defining description of the atom in the
same way that the three laws of English physicist Isaac Newton defined
classical mechanics and the way that the equations of British physicist James
Clerk Maxwell described electrodynamics. Instead, each new discovery about the
structure of the atom only made atomic structure more complicated. Much of
Schrödinger’s later work was concerned with philosophy, particularly as applied
to physics and the atom.

**Microsoft ® Encarta ® Reference Library 2003.** ©
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**Schrödinger,
Erwin**

**b****. Aug. 12, 1887, Vienna, Austria**

**d****. Jan. 4, 1961, Vienna **

Austrian theoretical physicist who contributed to the wave theory of matter and to other
fundamentals of quantum mechanics. He shared the 1933 Nobel Prize for Physics with the British
physicist P.A.M. Dirac.

**Schrödinger** entered the University of Vienna in 1906 and obtained his doctorate
in 1910, upon which he accepted a research post at the university's Second
Physics Institute. He saw military service in World War I and then went to the
University of Zürich in 1921, where he remained for
the next six years. There, in a six-month period in 1926, at the age of 39, a
remarkably late age for original work by theoretical physicists, he produced
the papers that gave the foundations of quantum wave mechanics. In those papers
he described his partial differential equation that is the basic equation of
quantum mechanics and bears the same relation to the mechanics of the atom as
Newton's equations of motion bear to planetary astronomy. Adopting a proposal
made by Louis de Broglie in 1924 that particles of
matter have a dual nature and in some situations act like waves, **Schrödinger**
introduced a theory describing the behaviour of such a system by a wave
equation that is now known as the **Schrödinger** equation. The solutions to **Schrödinger**'s equation,
unlike the solutions to Newton's equations, are wave functions that can only be
related to the probable occurrence of physical events. The definite and readily
visualized sequence of events of the planetary orbits of Newton is, in quantum
mechanics, replaced by the more abstract notion of probability. (This aspect of
the quantum theory made **Schrödinger** and several other physicists
profoundly unhappy, and he devoted much of his later life to formulating
philosophical objections to the generally accepted interpretation of the theory
that he had done so much to create.)

In 1927 **Schrödinger**
accepted an invitation to succeed Max Planck, the inventor of the quantum hypothesis,
at the University of Berlin, and he joined an extremely distinguished faculty
that included Albert Einstein. He remained at the university until 1933, at
which time he reached the decision that he could no longer live in a country in
which the persecution of Jews had become a national policy. He then began a
seven-year odyssey that took him to Austria, Great Britain, Belgium, the
Pontifical Academy of Science in Rome, and--finally in 1940--the Dublin
Institute for Advanced Studies, founded under the influence of Premier Eamon de Valera, who had been a
mathematician before turning to politics. **Schrödinger** remained in
Ireland for the next 15 years, doing research both in physics and in the
philosophy and history of science. During this period he wrote *What** Is Life? *(1944), an
attempt to show how quantum physics can be used to explain the stability of
genetic structure. Although much of what **Schrödinger** had to say
in this book has been modified and amplified by later developments in molecular
biology, his book remains one of the most useful and profound introductions to
the subject. In 1956 **Schrödinger** retired and returned to Vienna as
professor emeritus at the university.

Of all of the
physicists of his generation, **Schrödinger** stands out because of his
extraordinary intellectual versatility. He was at home in the philosophy and
literature of all of the Western languages, and his popular scientific writing
in English, which he had learned as a child, is among the best of its kind. His
study of ancient Greek science and philosophy, summarized in his *Nature and
the Greeks *(1954), gave him both an admiration for the Greek invention of
the scientific view of the world and a skepticism
toward the relevance of science as a unique tool with which to unravel the
ultimate mysteries of human existence. **Schrödinger**'s own metaphysical
outlook, as expressed in his last book, *Meine**
Weltansicht *(1961; *My View of the World*),
closely paralleled the mysticism of the Vedanta.

Because of his
exceptional gifts, **Schrödinger** was able in the course of his life to
make significant contributions to nearly all branches of science and
philosophy, an almost unique accomplishment at a time when the trend was toward
increasing technical specialization in these disciplines.

**Schrödinger
equation**

the fundamental equation of the science
of submicroscopic phenomena known as quantum
mechanics. The equation, developed (1926) by the Austrian physicist Erwin Schrödinger, has the same
central importance to quantum mechanics as Newton's laws
of motion have for the large-scale phenomena of classical mechanics.

Essentially a wave
equation, the Schrödinger equation describes the form of the probability waves
(or wave functions [*see* de Broglie wave])
that govern the motion of small particles, and it specifies how these waves are
altered by external influences. Schrödinger established the correctness of the
equation by applying it to the hydrogen atom, predicting many of its properties
with remarkable accuracy. The equation is used extensively in atomic, nuclear,
and solid-state physics.

**Schrödinger's
wave mechanics**

*from*** quantum mechanics**

**Schrödinger** expressed Broglie's hypothesis
concerning the wave behaviour of matter in a mathematical form that is
adaptable to a variety of physical problems without additional arbitrary
assumptions. He was guided by a mathematical formulation of optics, in which the straight-line
propagation of light rays can be derived from wave motion when the wavelength
is small compared to the dimensions of the apparatus employed. In the same way,
**Schrödinger** set out to find a wave equation for matter that would give
particle-like propagation when the wavelength becomes comparatively small.
According to classical mechanics, if a particle of mass *m _{e}* is
subjected to a force such that its potential energy is

It is assumed
that the particle is bound--*i.e.,* confined by the potential to a certain
region in space because its energy *E* is insufficient for it to escape.
Since the potential varies with position, two other quantities do also: the
momentum and, hence, by extension from the Broglie
relation, the wavelength of the wave. Postulating a wave function (*x,y,z*) that varies with
position, **Schrödinger** replaced *p* in the above energy equation
with a differential operator that embodied the Broglie
relation. He then showed that satisfies
the partial differential equation

This is the
(time-independent) **Schrödinger** wave equation of 1926, which established quantum mechanics
in a widely applicable form. An important advantage of **Schrödinger**'s
theory is that no further arbitrary quantum conditions need be postulated. The
required quantum results follow from certain reasonable restrictions placed on
the wave function--for example, that it should not become infinitely large at
large distances from the centre of the potential.

**Schrödinger** applied his equation to the hydrogen atom, for which the
potential function, given by classical electrostatics, is proportional to -*e*^{2}/*r*,
where -*e* is the charge on the electron. The nucleus (a proton of charge *e*)
is situated at the origin, and *r* is the distance from the origin to the
position of the electron. **Schrödinger** solved the equation for this
particular potential with straightforward, though not elementary, mathematics.
Only certain discrete values of *E* lead to acceptable functions
.
These functions are characterized by a trio of integers
*n, l, m*, termed quantum numbers. The values of *E*
depend only on the integers *n* (1, 2, 3, etc.) and are identical with
those given by the Bohr theory. The quantum numbers *l*
and *m* are related to the angular momentum of the electron; *l*(*l* + 1) is the magnitude of the angular
momentum, and *m* is its component along some physical direction.

The square of the
wave function, ^{2},
has a physical interpretation. **Schrödinger** originally supposed that the
electron was spread out in space and that its density at point *x,y,z* was given by the
value of ^{2}
at that point. Almost immediately Born proposed what is now the
accepted interpretation--namely, that ^{2}
gives the probability of finding the electron at *x,y,z*. The distinction between the two
interpretations is important. If ^{2}
is small at a particular position, the original interpretation
implies that a small fraction of an electron will always be detected there. In Born's interpretation, nothing will be detected there most
of the time, but, when something is observed, it will be a whole electron.
Thus, the concept of the electron as a point particle moving in a well-defined
path around the nucleus is replaced in wave mechanics by clouds that describe
the probable locations of electrons in different states.