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Erwin Schrodinger
The Founder of Quantum Wave Mechanics
 
 
 
Dr Subodh Mahanti

 

“The introduction of wave mechanics stands…as Schrodinger’s monument and a worth one.”

The Times

“Schrodinger never liked the generally accepted dual description of atomic physics in terms of waves and particles, as proposed by Bohr, Heisenberg and Born. He tried to set up a theory in terms of waves only. Like Einstein, he sought throughout all his life to unify gravitation and electromagnetism.”

Mauro Dardo


“His (Schrodinger’s) private life seemed strange to bourgeois people like ourselves. But all this does not matter. He was a most lovable person, independent, amusing, temperamental, kind and generous, and had a most perfect and efficient brain.”

Max Born



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