References D1 to D9 are to colour slides, not included in this document.
References F1 to F22 are to overhead transparencies, of which all but the
last four are included either as equations within the text or as Figures.
The scientific and personal links Dublin and Vienna are long-standing. Schrödinger is only one very prominent example. The work of Schrödinger in Dublin is well documented, I want to add only some personal remarks. Furthermore I want to show the importance of him for our daily scientific life in physics and chemistry.
I am coming from the wrong institution, namely the "TECHNISCHE HOCHSCHULE", now "Technical University" (TU), founded in 1815. Our Café, which is located in our new physics building, bears his name (Dl)(D2). One of his grandfathers has been full professor of applied chemistry at our TU. Originally he wanted therefore to start his studies at our university. Finally, his work, however was centred at the University of Vienna, founded 1365. There he became assistant before the first world war, professor, however, only in 1956, some years before his death. He was born in the district "Erdberg", slightly outside of the centre of Vienna. I am living in the same district for more than 50 years (D3).
Schrödinger got a private education until he came to the "Akademisches Gymnasium" (High School) in 1898. I attended this school some time after the 2nd World war (D4). It is still today one of the best high schools in Vienna and stresses classical culture, including the Greek and Latin languages. Here he acquired his everlasting love for poetry and the arts. He used e.g. citations from Goethe extensively in his book "What is Life".
At the University of Vienna, there is still a so called "Erwin Schrödinger Zimmer" (DS). Behind this door, however, is just a small exhibition of his papers (D6).
His scientific and some personal legacy is kept at the physics library at the University of Vienna, next to the works of Ludwig Boltzmann (D7). Schrödinger was influenced by Boltzmann, but he was not his student, since Schrödinger started his studies in the fall of 1906, while Boltzmann died in the summer of 1906. The successor of Boltzmann, Hasenöhrl, however, passed the ideas of Boltzmann and his own to Schrödinger. (Hasenöhrl was also my predecessor from 1905 to 1908). A class-mate of Schrödinger was Hans Thirring, later professor of theoretical physics at the university. His son Walter Thirring, now also professor of theoretical physics at the university, spent some years after 1945 with Schrödinger in Dublin. So did Otto Hittmair, many years my colleague at the Technical University and now still vice-president of the Austrian Academy of Science.
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For 24 years I am responsible for the Institut für Experimentalphysik at the Technical University. This institute is now located in the new physics building, I have shown before. In the library of our institute we have a collection of 30 reprints of scientific works by Schrödinger from 1912 to 1933. They have been collected by my predecessor Prof. Heinrich Mache, head of the Institut für Experimentalphysik from 1908 until 1946.
The first paper in our collection is the paper "Zur kinetischen Theorie des Magnetismus (Einfluss der Leitungselektronen.)" [The kinetic theory of magnetism. The influence of the conduction electrons]. H. Mache was obviously not interested in magnetism, because our copy has never been opened since 1912 (Fl).
This paper is concerned with diamagnetism. Diamagnetism, measured as a repulsion of matter in an inhomogeneous magnetic field, is common to all materials. This paper tries to explain diamagnetism by a mixture of Langevin paramagnetism (the attraction of materials in an inhomogeneous magnetic field) and the diamagnetism of the conduction electrons. We now know, that the efforts of Schrödinger had to be in vain, because diamagnetism can not be understood without quantum physics, which Schrödinger did not take into account. I cite this early paper (Schrödinger was an assistant at the university of Vienna at this time. His age was 25. Two years earlier he had finished his doctorate) because he argued during his life magnetism to be one basic phenomenon to be understood.
Now, however, I want to stress the scientific relations of Schrödinger to my own scientific interests, especially magnetism. Also in his lectures "What is life ?" Schrödinger used magnetism as an example (F2). However, most important for magnetism are his revolutionary papers entitled "Quantisierung als Eigenwertproblem" ("Quantisation as a problem of eigenvalues"), containing the foundations of the wave mechanics. These papers have been written in 1926 Zurich. (F3)(F4)
My personal relations with Dublin and especially the Trinity College are also based on magnetism, the interest in Rare Earth intermetallics and permanent magnets which I share with Prof. Mike Coey. Therefore I want to speak a little bit on this subject common to Dublin and Vienna.
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This question is nearly as complicated to answer as the question "What is life?" Naturally it is not as important. Magnetism has been a subject for speculation since several thousand years. Gilbert around the year 1600 summarised many experimental facts, still valid today. Applications of magnetism slowly emerged, especially in the connection with electrical engineering. But only quantum mechanics was able to explain magnetism. The already cited paper by Schrödinger is typical for the difficulties to explain even the most simple experimental facts, connected with magnetism.
Only in the last 20 to 30 years a breakthrough in the understanding and the applications of magnetism occurred.
We are surrounded all our life by the magnetic field of the earth, we are also producing in our body by means of currents flowing in our heart, our brain and our nerves magnetic fields, which can now be measured with great accuracy (by means of applied superconductivity).
We are usually not aware, that magnetic materials are part of our everyday life. Soft magnetic materials are at the core of all electric motors, transformers etc.. Magnetic storage materials as floppy discs and hard discs are indispensable parts of all computers. Hard magnetic materials are used in many electrical devices. Most cars contain several hundred of permanent magnets.
There are different basic kinds of magnetism known:
The already cited a) diamagnetism and b) paramagnetism, which are characteristic
for all kinds of gaseous, liquid and solid materials.
c) Ferro- ferri and antiferromagnetism and
d) still more complicated kinds of magnetic ordering are typical for special
solids, denominated "MAGNETIC MATERIALS".
All these latter forms of magnetism necessitate a magnetic moment. This moment is linked to the structure of the atoms and can only be understood by quantum mechanics. The complicated interplay of the moments formed by the rotation of the electron itself (spin) and of the moments arising from the movement of the electrons in orbits (orbital moment) form the total magnetic moment of an atom.
This moment can still be modified by the presence of other magnetic moments and the electrical charges in the crystal lattice. By describing the formation of moments in such a way, namely "rotation" and "movement on orbits" I have used implicitly Bohr's model, which was superceded by Schrödinger or at least explained by him and his colleagues. The discussion between Bohr and Schrödinger on the correct understanding of quantum physics lasted all their lifetime.
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The common interest in magnetism of Dublin and Vienna is based on the magnetism of Rare Earth metals and compounds. Rare Earth metals as e.g. Lanthanum, Cerium, Neodymium, Europium, etc. are not rare. They are used in flint stones, catalysts, the red colour of all television tubes and computer monitors, in permanent magnets etc.
Two questions arise:
a) Why are magnetic moments formed in these metals and ions? and
b) Why do magnetic moments form magnetic lattices?
Both questions can only be answered by quantum mechanics and especially the wave mechanics, founded by Schrödinger.
If we have a look on the magnetic moments, attributed to the trivalent rare earth ions, we see a regularity (F5). Several electrons are combined in such a way, that a collective interaction takes place, resulting in a definite magnetic moment. The Hund's rules of 1925 (F. Hund will be 100 years old next year) allow a calculation of the moment. The explanation of theses rules, however, are given by the Schrödinger equation.
There are several different notations of the most simple Schrödinger equation possible, one is given on the cross on top of his grave in Alpbach, Tyrol namely (D6) (F6)
Schrödinger was aware from the beginning, that special relativity had to be taken into account to calculate the energy levels e.g. of the hydrogen atom. He submitted late in 1925 to "Annalen der Physik" a relativistic equation, similar to the now well known Klein-Gordon equation, namely (F7)
This equation, however, was difficult to evaluate and led to results, not in agreement with experiment. Therefore, he withdrew his paper and replaced it by his paper "Quantisierung als Eigenwertproblem (Erste Mitteilung)". I have here a reprint from our folders. In this paper is printed on the second page, without much derivation the Schrödinger equation for the hydrogen atom. Most students, until today are not proceeding much beyond this formula (F8).
This formula, added with the property of the electron to bear a spin (Pauli-formula) is still today the basis for most calculations of the basic properties of matter.
Calculations of the square of the wave function
are equivalent to a calculation of the probability for the presence of
an electron. The allowed energy values ("EIGENVALUES") E
are characteristic for the stable states of matter.
Many calculations of Psi (the wave function) and E are performed by theoretical solid state physicists and theoretical chemists, based on extensions of the Schrödinger equation. Nowadays improvements of the mathematical methods and especially of the computers, make it possible to calculate sophisticated properties of matter, including magnetic properties.
The figure (F9) shows the radial distribution of the wave functions of Gadolinium, the most typical rare earth atom. One can see, that the electrons according to this calculation, based on the Hartree-Fock formula, which is derived from the Schrödinger equation, are smeared out in space. The resulting quantum numbers and the resulting magnetic moments of the trivalent rare earth have already been shown.
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By intermetallic compounds we understand an alloy with a distinct composition, as e.g. RAl2, YCo5, Nd2Fe14B, Sm2Fe17 etc. The presence of quasi-free conduction electrons makes the interaction between the 4f electrons, deeply buried in the electron shell of the different R-atoms, possible. These 4f electrons are responsible for the different magnetic moments of the R-atoms and also for the ordering temperatures of intermetallics with different R-atoms (F10).
Most important are intermetallics where R-elements are combined with 3d-elements as e.g. Mn, Fe, Co or Ni. In this case the total magnetic properties are a combination of the properties of the R-atoms and the 3d-atoms, locked in a specific crystal structure. This complicated situation manifests itself e.g. in the Curie or ordering temperatures (F11)(F12) (F13).
The presence of different crystal electrical fields in a R-3d intermetallic results in a complicated situation for the energy levels and their splitting (F14). In principle all these levels and their interaction can be calculated by the Schrödinger equation and its derivatives. Recently also the magnetic anisotropy and the corresponding anisotropy constant K1 can be calculated, which forms the basis for all modern permanent magnets.
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In this same lecture hall in the last 10 years many scientific lectures have been given in the framework of CEAM, i.e. Concerted European Action on Magnets. This project was successfully guided by Mike Coey and had the task, to promote and develop new permanent magnets in Europe.
I was engaged with permanent magnets since 30 years. In 1966 Karl Strnat and co-workers found that compounds of the type YCo5 or SmCo5 are magnetically anisotropic and have a large anisotropy field (F15). Subsequently the Rare Earth magnets based on SmCo5 or Sm2Co17 have been developed. They have revolutionised the use of permanent magnets in mechanical devices, electronics, computers etc.
The high price of these magnets, however, restricted their use. In 1983 a new type of permanent magnets, based on Nd2Fe14B have been developed. This prompted the CEAM project, where Dublin was the headquarters.
The crystal structure of the basic compound is quite complicated (F16). Therefore many investigations had to be done, to establish some understanding of the contribution of the different atomic species in this compound to the total magnetic properties. A new magnetic compound, namely Sm2Fe17Nx was developed in Dublin by Mike Coey and his group.
A magnetically anisotropic compound, however, does not automatically constitute a permanent magnet. Studies of the forming of a permanent magnet by sintering, annealing and magnetising etc. are necessary. Another possibility is the production of bonded permanent magnets, where a proper combination of magnetic materials and binders (usually organic resins) is necessary, if a permanent magnet with high quality and useful properties shall be developed. Further work is necessary to establish a new permanent magnet material in industry. Most of these complicated multi-disciplinary efforts have been directed by Trinity College in recent years, as far as Europe is concerned. As a result, the European science and also the European industry has been promoted considerably in different fields. All this has been documented in many reports, scientific papers, patents, books, conferences etc., which are available world-wide. Probably everyone in this room has several of these modern permanent magnets in his home, office and car, without knowing the connection to Trinity College.
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On May 15th 1955 the State Treaty was signed in Vienna, which resulted in the end of the occupation of Austria by the four allies. In June 1955 Schrödinger was invited to return to his Alma Mater as Professor of Theoretical Physics. On Friday April 13th, 1956 he gave his inaugural lecture at the "Auditorium maximum". I attended this lecture and I have here with me the manuscript. The political "high society" was present. Schrödinger spoke on "Die Krise des Atombegriffes" (The crisis of the concept of atoms) (F17).
He discussed the discrepancies between the wave picture and the complementarity principle of Niels Bohr. Schrödinger remarked that this picture, unfortunately, has succeeded. He never agreed to this concept, which now is generally accepted.
In this talk he referred to his teacher Boltzmann, who gave statistical mechanics and especially entropy a sound foundation. His formula
S = k logW
S = entropy
k = Boltzmann's constant
W = Wahrscheinlichkeit (probability)
is given on top of his gravestone (D7) (F18). Schrödinger, in the tradition of Boltzmann referred to the concept of entropy extensively in his lectures "What is life?" by using the term "Negentropy" or negative entropy. The connection of this term with the free energy and free enthalpy, responsible for the stability of all matter and the possibility for chemical reactions and finally also life, is still under discussion.
Schrödinger gave some more lectures in Vienna, but soon retired to Alpbach, Tyrol. He died in Vienna on January 4, 1961.
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Today Schrödinger is well known to everybody in Austria, because he faces the 1000 Schilling bill. (F19) He is only second to Mozart, who is on the 5000 Schilling bill, and has 20 times the value of Siegmund Freud, who is on the 50 Schilling bill (F20) (F21).
However it is my experimental finding, that less than 0.1% of the Austrian population know what Schrödinger had done and what impact he still has on science and culture. Furthermore our Austrian national bank has used Psi as a decorative element, completely unknown to everybody. Bohr's model is also present in the form of electron orbits (against the advice of Prof. Otto Hittmair). Most Austrians therefore assume, that Schrödinger is the inventor of Bohr's model, now a synonym for "atomic". We don't know if Schrödinger is happy with this mix up. Anyhow, he, for sure, wanted to supersede this kind of thinking in distinct electron orbits.
Therefore Schrödinger is known to literally everybody in Austria, but nobody understands his work. This is typical good old Austrian tradition. At Trinity College it will be different due to this ceremony. Many thanks for this.
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(Only some, not frequently cited sources are given)
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(Not included in this document)
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