Erwin Schrodinger was one of the main architects of quantum mechanics.
Schrodinger developed the wave mechanics. It became the second formulation
of quantum mechanics. The first formulation, called matrix mechanics,
was developed by Werner Heisenberg. Schrodinger’s wave equation
(or Schrodinger equation) is one of the most basic equations of
quantum mechanics. It bears the same relation to the mechanics of
the atom as Newton’s equations of motions bear to planetary
astronomy. However, unlike Newton’s equations, which result
definite and readily visualized sequence of events of the planetary
orbits, the solutions to Schrodinger’s wave equation are wave
functions that can only be related to probable occurrence of physical
events. Schrodinger’s wave equation is a mathematically sound
atomic theory. It is regarded by many as the single most important
contribution to theoretical physics in the twentieth century. Schrodinger’s
book, “What is Life?” led to progress in biology.
Schrodinger was an unconventional man. Throughout his life he traveled
with walking-boots and rucksack and for this he had to face some
difficulty in gaining entrance to the Solvay Conference for Nobel
laureates. Describing the incident Paul Dirac wrote: “When
he went to the Solvay Conferences in Brussels, he would walk from
the station to the hotel…carrying all his luggage in a rucksack
and looking so like a tramp that it needed a great deal of argument
at the reception desk before he could claim a room.”
Schrodinger was born on August 12, 1887 in Vienna.
His father Rudolf Schrodinger, who came from a Bavarian family,
which had come to Vienna generations ago, was a highly gifted man.
After studying chemistry at the Technical College in Vienna, Rudolf
Schrodinger devoted himself for years to Italian painting and then
he decided to study botany. He published a series of research papers
on plant phylogeny.
Rudolf Schrodinger had inherited a small but profitable
business manufacturing linoleum and oilcloth. Schrodinger’s
mother, Georgine Schrodinger (nee Bauer) was the daughter of Alexander
Bauer, an able analytical chemist and who became a professor of
chemistry at the Technical College, Vienna. Schrodinger was always
grateful to his father for giving him a comfortable upbringing and
a good education. He described his father ‘as a man of broad
culture, a friend, teacher and inexhaustible partner in conversation.’
Schrodinger was taught by a private tutor at home
until he entered the Akademisches Gymnasium in 1898. He passed his
matriculation examination in 1906. At the Gymnasium, Schrodinger
was not only attracted to scientific disciplines but also enjoyed
studying grammar and German poetry. Talking about his impression
at the Gymnasium Schrodinger later said: “I was a good student
in all subjects, loved mathematics and physics, but also the strict
logic of the ancient grammars, hated only memorizing incidental
dates and facts. Of the German poets, I loved especially the dramatists,
but hated the pedantic dissection of their works.” He was
an outstanding student of his school. He always stood first in his
class. His intelligence was proverbial. One of his classmates commenting
on Schrodinger’s ability to grasp teachings in physics and
mathematics said: “Especially in physics and mathematics,
Schrodinger 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 Schrodinger immediately
to the blackboard and to set him problems, which he solved with
playful facility.”
In 1906, Schrodinger joined the Vienna University.
Here he mainly focused in the course of theoretical physics given
by Friedrich Hasenohrl, who was Boltzmann’s student and successor.
Hasenhorl gave an extended cycle of lectures on various fields of
theoretical physics transmitting views of his teacher, Boltzmann.
Schrodinger received his PhD in 1910. His dissertation was an experimental
one. It was on humidity as a source of error in electroscopes. The
actual title of the dissertation was “On the conduction of
electricity on the surface of insulators in moist air.” The
work was not very significant. The committee appointed for examining
the work was not unanimous in recommending him for the degree. After
receiving his PhD, he undertook his voluntary military service.
After returning from military service in autumn 1911, he took up
an appointment as an assistantship in experimental physics at the
University of Vienna. He was put in charge of the large practical
class for freshmen. Schrodinger had no love for experimental work
but at the same time he valued the experience. He felt that it taught
him “through direct observation what measuring means.”
He started working in theoretical physics by applying Boltzmann-like
statistical-mechanical concepts to magnetic and other properties
of bodies. The results were not very significant. However, based
on his work he could earn his advanced doctorate (Habilitation).
At the beginning of the First World War, Schrodinger
was called up for active service. He was sent to the Italian border.
It was at the warfront that Schrodinger learned about Einstein’s
general theory of relativity and he immediately recognized its great
importance. While in war field it was not possible for Schrodinger
to keep him fully abreast of the developments in theoretical physics.
However, he continued his theoretical work. He submitted a paper
for his publication from his position on the Italian front. In the
spring of 1917, Schrodinger was transferred to Vienna, where he
again could start scientific work.
The First World War resulted in total collapse
of the economy of Austria. It also ruined Schrodinger’s family.
Schrodinger had no option other than to seek a career in the wider
German-language world of Central Europe. Between spring 1920 and
autumn 1921, Schrodinger took up successively academic positions
at the Jena University (as an assistant to Max Wien, Wilhelm Wein’s
brother, at the Stuttgart Technical University(extraordinary professor),
the Breslau University (ordinary professor), and finally at the
University of Zurich, where he replaced von Laue. Soon after arriving
at Zurich, Schrodinger was diagnosed with suspected tuberculosis
and he was sent to an alpine sanatorium in Arosa to recover. While
recuperating at Arosa, Schrodinger wrote one of his most important
papers, “On a Remarrkable Property of the Quantised Orbits
of an Electrn.’ At Zurich he stayed for six years. This was
his most productive and beautiful period of his professional life.
It was at Zurich that Schrodinger made his most
important contributions. He first studied atomic structure and then
in 1924 he took up quantum statistics. However, the most important
moment of his professional career was when he came across Louis
de Broglie’s work. On November 03, 1925, Schrodinger wrote
to Einstein: “A few days ago I read with great interest the
ingenious thesis of Louis de Broglie, which I finally got hold of…”
And then on 16th November he wrote: “I have been intensely
concerned these days with Louis de Broglie’s ingenious theory.
It is extraordinarily exciting, but still has some very grave difficulties.”
After reading de Broglie’s work Schrodinger began to think
about explaining the movement of an electron in an atom as a wave
and eventually came out with a solution. He was not at all satisfied
with the quantum theory of the atom developed by Niels Bohr, who
was not happy with the apparently arbitrary nature of a good many
of the quantum rules. Schrodinger did not like the generally accepted
dual description of atomic physics in terms of waves and particles.
He eliminated the particle altogether and replaced it with wave
alone. His first step was to develop an equation for describing
the movement of electrons in an atom. The de Broglie equation giving
the wavelength ?=h/mv (where h is the Planck constant and mv the
momentum) represented too simple a picture to match the reality
particularly with the inner atomic orbits where the attractive force
of the nucleus would result in a very complex and variable configuration.
Schrodinger eventually succeeded in developing his famous wave equation.
His equation was very similar to classical equations developed earlier
for describing many wave phenomena—sound waves, the vibrations
of a string or electromagnetic waves. In Schrodinger’s wave
equation there is an abstract entity, called the wave function and
which is symbolized by the Greek letter ?(psi). When applied to
the hydrogen atom, Schrodinger’s wave equation yielded all
the results of Bohr and de Broglie. However, despite the considerable
predictive success of Schrodinger’s wave mechanics, Schrodinger’s
had to overcome certain problems. First how he as going to attach
some physical meaning to the ideas of an electron if it was nothing
but wave and also he had to show what exactly represented by the
wave function.
Schrodinger unsuccess- fully tried to account
these. He tried to visualize electron as `wave packets’ made
up of many small waves so that these wave packets would behave in
the same way as a particle in classical mechanics. However, these
packets were later shown to be unstable. He interpreted the wave
function as a measure of the spread of an electron. But this was
also not acceptable. The interpretation was provided by Max Born.
He stated that the wave function for a hydrogen atom represents
each of its physical states and it can be used to calculate the
probability of finding the electron at a certain point in space.
What does it mean? It means that if the wave function is nearly
zero at a certain point then the probability of finding the electron
there is extremely small. But where the wave function is large the
probability of finding the electron is very large. The wave mechanics
cannot be used to determine the motion of a particle or in other
words its position and velocity at any given moment. The wave equation
simply tells us how the wave function evolves in space and time
and the value of the wave function would determine the probability
of finding the electron in a particular point of space.
He published his revolutionary work in a series
of papers in 1926. Schrodinger’s wave equation was the second
theoretical explanation for the movement of electrons in an atom,
the first being Werner Heisenberg’s matrix mechanics. Schrodinger’s
approach was preferred by many physicists as it could be visualized.
On the other hand Heisenberg’s approach was strictly mathematical
and it involved such a complex mathematics that it was difficult
to understand. Physicists appeared to be divided into two groups.
However, soon Schrodinger showed that the two theories were identical
but expressed differently.
Schrodinger’s students at Zurich found his
lectures ‘extremely stimulating and impressive.’ One
of his students, who attended his lectures, later recalled: “…At
the beginning he stated the subject and then gave a review of how
one had to approach it, and then he started exposing the basis in
mathematical terms and developed it in front of our eyes. Sometimes
he would stop and with a shy smile confess that he had missed a
bifurcation in his math |