Download Erwin Schrödinger (1887 – 1961)

Erwin Schrödinger (1887 – 1961)
Erwin Schrödinger was born in Vienna, Austria on August 12, 1887. His
father, Rudolf Schrödinger, ran a small linoleum factory which he had inherited
from his own father. His mother, Georgine Bauer was half English and half
Austrian. Erwin was the only child of the couple. Due to his mother’s heritage,
the young Erwin learned both German and English at the same time. His parents
chose not to enroll him in an elementary school and instead provided private
tutors. At the age of ten in 1898, which was rather late for that time, he was
enrolled in the Akademisches Gymnasium. He enjoyed German literature but
excelled in Mathematics and in Physics. One of his classmates at the Gymnasium wrote: “Especially in
physics and mathematics, Schrödinger had a gift for understanding that allowed him, without any
homework, immediately and directly to comprehend all the material during the class hours and to apply it.
After the lecture ... it was possible for [our professor] to call Schrödinger immediately to the blackboard
and to set him problems, which he solved with playful facility. “
Schrödinger graduated from the Gymnasium in 1906 and entered the University of Vienna that
same year. He chose to study theoretical physics and within this field, he studied analytical mechanics,
applications of partial differential equations to dynamics, eigenvalue problems, Maxwell's equations and
electromagnetic theory, optics, thermodynamics, and statistical mechanics. Though he continued to study
Mathematics at the University, theoretical physics would have the greatest influence on him.
In 1910, only four years after entering the University of Vienna, Schrödinger was awarded his
doctorate for the dissertation On the conduction of electricity on the surface of insulators in moist air.
Instead of directly applying for academic positions, Schrödinger chose instead to volunteer for military
service in a position of fortress artillery. Only after completing this commitment did he pursue his
academic aspirations. He was first appointed to an assistantship at Vienna but, rather surprisingly, in
experimental physics rather than theoretical physics. He later said that his experiences conducting
experiments proved an invaluable asset to his theoretical work since it gave him a practical framework in
which to set his theoretical ideas. This work as an experimental physicist completed his post-doctoral
training and he was thus qualified to lecture at German universities.
Schrödinger produced his first significant paper in 1914 elaborating on Boltzmann’s ideas. He was
then drafted into the Army on the Italian front in WWI. He did not waste his time however, sending in
manuscripts from both the Italian front and the subsequent posting in Hungary. In 1917, he returned to
Vienna where he taught meteorology and conducted further research. It is during this period that he
produced his first writings on quantum theory.
After the war, Schrödinger wished to marry Anny Bertel. At this point, even with the new
appointment to an associate professorship, Anny made more money per month as a secretary than he did so
he turned down the position and took one at Jena followed closely by a chair in Stuttgart and then one in
Breslau (all within 18 months!). In 1921, he made yet another move to a chair in Zurich. Here was the
intellectual atmosphere that would foster his greatest contributions. When he arrived in Zurich, he turned
his attention from color vision to atomic structure and quantum statistics. He read de Broglie’s work in
1925, a turning point in his work. He gave a lecture on de Broglie’s work in late 1925 and a member of the
audience, one of Sommerfeld’s students, suggested that there should be a wave equation. Within a week,
Schrödinger’s equation was born.
d2 Ψ + 8πm * (E – V) Ψ = 0
d x2
h2
d2 refers to the second derivative with respect to x, x refers to position, E to energy, V to potential energy
and Ψ to Schrödinger’s wave function.
With this, Schrödinger would enhance and continue what Heisenberg had started with Matrix
mechanics: the New Quantum Theory. The solution to the equation is a wave that described the quantum
aspects of the system. However, the physical interpretation would become a problem. Since Schrödinger
had studied eigenvalues or certain values, he knew that the solution lay in finding the correct functions that,
when superimposed, would produce the desired solution. He found that the wave functions of the
individual states are natural harmonics of each other; their frequencies are related by integer ratios. What
does this mean? It means that eigenvalue functions underlie the quantization of atomic systems that are
seen. We see quantum jumps because that is the sum (replacement wave) of superimposed waves of each
individual state of the quantum system. Bohr, Sommerfeld and Heisenberg’s quantum numbers were all
related as the number of nodes in a vibrating system. This new field was called wave mechanics.
Schrödinger described with his equation the hydrogen atom’s spectrum and showed that the
integers derived from the wave solution in 3D correspond exactly to n, l and m. He hated the quantum
jumps described by Bohr and now he could explain the observations (spectra) without resorting to that
“silliness”. He did make an unsuccessful attempt at discounting the existence of particles and reconciling
quantum mechanics with classical physics but that was dispelled by Lorentz and Heisenberg (QT, p.140143). After speaking to Heisenberg, he discovered that wave mechanics and matrix mechanics were
completely equivalent mathematically. For his discovery of wave mechanics, Schrödinger won the Nobel
Prize for Physics in 1933.
Perhaps the equation above seems daunting, but the most confusing of Schrödinger’s speculations
was yet to come. Max Born had shown that the wave function, Ψ, is the probability amplitude for an
electron in the state n to scatter into the direction m. The function represented its own intensity wave and
when it was squared, he postulated, it represented the physical probability of that particle’s presence or the
existence of a quantum state. Now, the electron cloud theory rather than set orbits, was introduced.
Schrödinger didn’t like this interpretation, he believed that Ψ represented a shadow wave that indicated
position. He tried to illustrate the absurdity of Born’s ideas by creating the cat thought experiment. This
involved a cat in a box. When we take a measurement, an observation, we can tell if the cat is alive or
dead. The idea of superposition of states would suggest that until we make the observation of death or life,
the cat is neither dead nor alive but both. This paradox is used to explain quantum theory and the
measurement dilemma.
Schrödinger was a very colourful character. He had numerous love affairs including one affair with
a colleague’s wife, Hilde March (wife of Arthur March) which produced a daughter Ruth. He had two
more daughters, each of different women with whom he had affairs. He and his wife Anny would never
have children though Anny cared for at least two of the extramarital daughters. Anny herself would have
significant extramarital affairs. The Schrödingers particularly enjoyed the Austrian Tyrol for their romantic
affairs. Erwin also wrote a book of poetry in 1946 that was not well received by connaiseurs of German
poetry.
Later in his career, Schrödinger became interested in how biology and physics were related. He
wrote What is Life? and Mind and Matter which attempted to explain genetics and psychology in the
context of quantum physics.
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References
A Hermann, Erwin Schrödinger - eine Biographie, Die Wellenmechanik (Stuttgart, 1963), 173-192.
http://www-groups.dcs.st-and.ac.uk/~history/Mathematicians/Schrodinger.html
McEnvoy, J.P. and Zarate O. 2000. Introducing Quantum Theory. USA: Totem books. p.132-147.
Moore, W.J. 1989. Schrödinger: life and thought. New York: Cambridge University Press.
Scott, W.T. 1967. Erwin Schrödinger: An Introduction to his Writings. Amherst, Massachusetts:
University of Massachusetts Press.