Franz Rellich
Encyclopedia
Franz Rellich was an Austrian
-Italian mathematician
.
He made important contributions in mathematical physics
, in particular for the foundations of quantum mechanics
and for the theory of
partial differential equation
s.
. He studied from 1924 to 1929 at the universities of Graz
and Göttingen
and received his doctor's degree in 1929 under Richard Courant
at Georg August University of Göttingen with the thesis about "Verallgemeinerung der Riemannschen Integrationsmethode auf Differentialgleichungen n-ter Ordnung in zwei Veränderlichen" ("Generalization of Riemann's integration method on differential equations of n-th order in two variables").
When in 1933 the great mathematical-physical tradition in Göttingen terminated with the Machtergreifung
of the Nazis
, Rellich, having taken an active position against Nazism, was among those forced to leave.
In 1934 he became Privatdozent
in Marburg
, in 1942 professor in Dresden
, and in 1946 director of the Mathematical Institute in Göttingen, being instrumental in its reconstruction. Jürgen Moser
was one of his students.
Rellich died in Göttingen
.
of linear operators on
Hilbert space
s: he studied the dependence of the spectral family
of a self-adjoint operator
on the parameter 
.
Although the origins and applications of the problem are in quantum mechanics
, Rellich's approach was completely abstract.
Rellich successfully worked on many partial differential equation
s with degeneracies.
For instance, he showed that in the elliptic case, the Monge-Ampère differential equation
, while not necessarily uniquely soluble, can have at most two solutions.
Particularly relevant to physics was Rellich's mathematical clarification of the outgoing Sommerfeld
conditions.
Austrians
Austrians are a nation and ethnic group, consisting of the population of the Republic of Austria and its historical predecessor states who share a common Austrian culture and Austrian descent....
-Italian mathematician
Mathematician
A mathematician is a person whose primary area of study is the field of mathematics. Mathematicians are concerned with quantity, structure, space, and change....
.
He made important contributions in mathematical physics
Mathematical physics
Mathematical physics refers to development of mathematical methods for application to problems in physics. The Journal of Mathematical Physics defines this area as: "the application of mathematics to problems in physics and the development of mathematical methods suitable for such applications and...
, in particular for the foundations of quantum mechanics
Quantum mechanics
Quantum mechanics, also known as quantum physics or quantum theory, is a branch of physics providing a mathematical description of much of the dual particle-like and wave-like behavior and interactions of energy and matter. It departs from classical mechanics primarily at the atomic and subatomic...
and for the theory of
partial differential equation
Partial differential equation
In mathematics, partial differential equations are a type of differential equation, i.e., a relation involving an unknown function of several independent variables and their partial derivatives with respect to those variables...
s.
Biography
Rellich was born in Tramin, then in the County of TyrolCounty of Tyrol
The County of Tyrol, Princely County from 1504, was a State of the Holy Roman Empire, from 1814 a province of the Austrian Empire and from 1867 a Cisleithanian crown land of Austria-Hungary...
. He studied from 1924 to 1929 at the universities of Graz
Graz
The more recent population figures do not give the whole picture as only people with principal residence status are counted and people with secondary residence status are not. Most of the people with secondary residence status in Graz are students...
and Göttingen
Göttingen
Göttingen is a university town in Lower Saxony, Germany. It is the capital of the district of Göttingen. The Leine river runs through the town. In 2006 the population was 129,686.-General information:...
and received his doctor's degree in 1929 under Richard Courant
Richard Courant
Richard Courant was a German American mathematician.- Life :Courant was born in Lublinitz in the German Empire's Prussian Province of Silesia. During his youth, his parents had to move quite often, to Glatz, Breslau, and in 1905 to Berlin. He stayed in Breslau and entered the university there...
at Georg August University of Göttingen with the thesis about "Verallgemeinerung der Riemannschen Integrationsmethode auf Differentialgleichungen n-ter Ordnung in zwei Veränderlichen" ("Generalization of Riemann's integration method on differential equations of n-th order in two variables").
When in 1933 the great mathematical-physical tradition in Göttingen terminated with the Machtergreifung
Machtergreifung
Machtergreifung is a German word meaning "seizure of power". It is normally used specifically to refer to the Nazi takeover of power in the democratic Weimar Republic on 30 January 1933, the day Hitler was sworn in as Chancellor of Germany, turning it into the Nazi German dictatorship.-Term:The...
of the Nazis
Nazism
Nazism, the common short form name of National Socialism was the ideology and practice of the Nazi Party and of Nazi Germany...
, Rellich, having taken an active position against Nazism, was among those forced to leave.
In 1934 he became Privatdozent
Privatdozent
Privatdozent or Private lecturer is a title conferred in some European university systems, especially in German-speaking countries, for someone who pursues an academic career and holds all formal qualifications to become a tenured university professor...
in Marburg
Marburg
Marburg is a city in the state of Hesse, Germany, on the River Lahn. It is the main town of the Marburg-Biedenkopf district and its population, as of March 2010, was 79,911.- Founding and early history :...
, in 1942 professor in Dresden
Dresden
Dresden is the capital city of the Free State of Saxony in Germany. It is situated in a valley on the River Elbe, near the Czech border. The Dresden conurbation is part of the Saxon Triangle metropolitan area....
, and in 1946 director of the Mathematical Institute in Göttingen, being instrumental in its reconstruction. Jürgen Moser
Jürgen Moser
Jürgen Kurt Moser or Juergen Kurt Moser was a German-American mathematician.-Professional biography:...
was one of his students.
Rellich died in Göttingen
Göttingen
Göttingen is a university town in Lower Saxony, Germany. It is the capital of the district of Göttingen. The Leine river runs through the town. In 2006 the population was 129,686.-General information:...
.
Contributions
Among Rellich's most important mathematical contributions are his work in the perturbation theoryPerturbation theory
Perturbation theory comprises mathematical methods that are used to find an approximate solution to a problem which cannot be solved exactly, by starting from the exact solution of a related problem...
of linear operators on
Hilbert space
Hilbert space
The mathematical concept of a Hilbert space, named after David Hilbert, generalizes the notion of Euclidean space. It extends the methods of vector algebra and calculus from the two-dimensional Euclidean plane and three-dimensional space to spaces with any finite or infinite number of dimensions...
s: he studied the dependence of the spectral family
of a self-adjoint operatorSelf-adjoint operator
In mathematics, on a finite-dimensional inner product space, a self-adjoint operator is an operator that is its own adjoint, or, equivalently, one whose matrix is Hermitian, where a Hermitian matrix is one which is equal to its own conjugate transpose...
on the parameter .Although the origins and applications of the problem are in quantum mechanics
Quantum mechanics
Quantum mechanics, also known as quantum physics or quantum theory, is a branch of physics providing a mathematical description of much of the dual particle-like and wave-like behavior and interactions of energy and matter. It departs from classical mechanics primarily at the atomic and subatomic...
, Rellich's approach was completely abstract.
Rellich successfully worked on many partial differential equation
Partial differential equation
In mathematics, partial differential equations are a type of differential equation, i.e., a relation involving an unknown function of several independent variables and their partial derivatives with respect to those variables...
s with degeneracies.
For instance, he showed that in the elliptic case, the Monge-Ampère differential equation
Monge-Ampère equation
In mathematics, a Monge–Ampère equation is a nonlinear second order partial differential equation of special kind. A second order equation for the unknown function u of two variables x,y is of Monge–Ampère type if it is linear in the determinant of the Hessian matrix of u and in the second order...
, while not necessarily uniquely soluble, can have at most two solutions.
Particularly relevant to physics was Rellich's mathematical clarification of the outgoing Sommerfeld
Arnold Sommerfeld
Arnold Johannes Wilhelm Sommerfeld was a German theoretical physicist who pioneered developments in atomic and quantum physics, and also educated and groomed a large number of students for the new era of theoretical physics...
conditions.
Sources
- Biographical notes by Göttingen University (in German)
- S. Gottwald, H.-J. Ilgauds, K.-H. Schlote (Hrsg.): Lexikon bedeutender Mathematiker. Verlag Harri Thun, Frankfurt a. M. 1990 ISBN 3-8171-1164-9