Josef Meixner

{{Short description|German theoretical physicist}} {{for|the Austrian Olympic shooter|Josef Meixner (sport shooter)}} {{Infobox scientist | name = Josef Meixner | native_name = | native_name_lang = | image =  | image_size = | alt = | caption = | birth_name =  | birth_date = {{birth date |1908|04|24|df=y}} | birth_place = Percha, Kingdom of Bavaria, German Empire | death_date = {{death date and age |1994|03|19 |1908|04|24|df=y}} | death_place = Aachen, Germany | resting_place = | resting_place_coordinates =  | other_names = | siglum = | citizenship = | fields = Physics | workplaces = {{plainlist| *University of Giessen *Humboldt University of Berlin *RWTH Aachen University }} | patrons = | alma_mater = Ludwig-Maximilians-Universität München | thesis_title = Die Greensche Funktion des wellenmechanischen Keplerproblems | thesis_url =  | thesis_year = 1931 | doctoral_advisor = Arnold Sommerfeld | academic_advisors = | doctoral_students = | notable_students = | known_for = {{plainlist| *Meixner distribution *Meixner polynomials *Meixner–Pollaczek polynomials }} | awards = | author_abbrev_bot = | author_abbrev_zoo = | spouse =  | partner =  | children = | signature =  | signature_alt = | website =  | footnotes = }} '''Josef Meixner''' (24 April 1908 – 19 March 1994) was a German theoretical physicist,<ref>{{cite journal|author=Schlögl, Friedrich|title=Obituary: Josef Meixner|journal=Physics Today|date=November 1994|volume=47|issue=11|pages=106|doi=10.1063/1.2808715 |doi-access=free}}</ref> known for his work on the physics of deformable bodies, thermodynamics, statistical mechanics, Meixner polynomials, Meixner–Pollaczek polynomials, and spheroidal wave functions.<ref name="Meixner">[http://cio.nist.gov/esd/emaildir/lists/opsfnet/msg00028.html Meixner] {{webarchive|url=https://web.archive.org/web/20060929023822/http://cio.nist.gov/esd/emaildir/lists/opsfnet/msg00028.html |date=2006-09-29 }} – CIO NIST</ref>

==Education== Meixner began his studies in theoretical physics with Arnold Sommerfeld at the Ludwig-Maximilians-Universität München in 1926. He was awarded his doctorate in 1931, with the submission of a thesis on the application of the Green function in quantum mechanics.<ref>[http://www.amphilsoc.org/library/guides/ahqp/bios.htm Sommerfeld Biography] {{webarchive|url=https://web.archive.org/web/20060927084229/http://www.amphilsoc.org/library/guides/ahqp/bios.htm |date=2006-09-27 }} – American Philosophical Society</ref><ref>[https://genealogy.math.ndsu.nodak.edu/html/id.phtml?id=48491 Meixner] – Mathematics Genealogy Project. Ph.D. Ludwig-Maximilians-Universität München 1931. Dissertation title: ''Die Greensche Funktion des wellenmechanischen Keplerproblems''.</ref>

==Career== Meixner taught at a high school for a few years. He was an assistant at the Institute of Theoretical Physics in Munchen until 1934. He worked with Salomon Bochner to determine that the Hermite polynomials were the only orthogonal polynomials <math>p_n(x)</math> with generating functions of the form <math>f(t)e^{xt} = \sum_{n=0}^{\infty}p_n(x)\frac{t^n}{n!}</math>. <ref name="butzer-koornwinder">{{cite journal |title= Josef Meixner: His life and his orthogonal polynomials |year= 2019 |doi= 10.1016/j.indag.2018.09.009 |arxiv= 1609.02588 |last1= Butzer |first1= Paul L. |last2= Koornwinder |first2= Tom H. |journal= Indagationes Mathematicae |volume= 30 |pages= 250–264 |s2cid= 119327238 }}</ref>

Meixner later wrote in his personal memoirs about his close friend, an Austrian Jew who came to Munich in 1929 and left for Princeton in 1933:

<blockquote>Bochner foresaw the coming political development very clearly, and I recall when we, surely at the end of 1932, stood before a bulletin board of the Voelkischer Beobachter and he said: ‘Now it is almost time that I must depart’. When I [at age 24] replied that then I would also like to leave, he replied: You remain here; nothing will happen to you and for us there are too few places in the world.<ref name="butzer-koornwinder"></ref></blockquote>

Meixner loosened the condition on the generating function and determined that <math>f(t)e^{xu(t)} = \sum_{n=0}^{\infty}p_n(x)\frac{t^n}{n!}</math> was satisfied by five classes of polynomials, known as the Hermite polynomials, Charlier polynomials, Laguerre polynomials, Meixner polynomials and Meixner-Pollaczek polynomials. He published this result in 1934.<ref>{{cite journal | title=Meixner, Josef. Orthogonale Polynomsysteme mit einer besonderen Gestalt der erzeugenden Funktion, J. London Math. Soc. 9 (1934), 6–13| journal=Journal of the London Mathematical Society |series=Second Series| year=1934| doi=10.1112/JLMS/S1-9.1.6| s2cid=123114348| last1=Meixner| first1=J.}}</ref>

In 1934, Meixner became an Assistant in theoretical physics to Karl Bechert at the University of Giessen. Also in 1934, he joined the Nazi paramilitary SA. In 1937, he became a Lecturer and also joined the Nazi party. From 1939 to 1941 he was a lecturer at the Humboldt University of Berlin. Serving in the German army, from September 1941 he was stationed at the weather station at Vadsø, Finnmark, Norway.<ref name="butzer-koornwinder"></ref>

In 1942, he was appointed “Extraordinary” Professor of theoretical physics and Director of the Institute of Theoretical Physics at the RWTH Aachen University in Germany. However, he could not take up this position until he was released from the armed forces in the summer of 1943. Meixner received a denazification certificate (Persilschein) with the help of his PhD advisor Sommerfeld, one of the few German scientists untainted with Nazi affiliation, who wrote that Meixner had never been a supporter of the Nazi system but in his circumstances it would have been very difficult for him to avoid joining the SA. Meixner was promoted to “Ordinary” Professor in 1949.<ref name="butzer-koornwinder"></ref>

After Sommerfeld's death in 1951, Meixner edited a volume and new editions of two other volumes of Sommerfeld's six-volume ''Vorlesungen über theoretische Physik''.

Meixner conducted research and taught graduate courses at the Institut für theoretische Physik of the RWTH Aachen University. Literature citations, as well as doctorates granted to his students, put Meixner at RWTH Aachen University, or just Aachen, for years in each of the decades from the 1950s until his death in 1994. He was known for his work on the physics of deformable bodies (rheology), thermodynamics, statistical mechanics, Meixner polynomials, Meixner-Pollaczek polynomials, and spheroidal wave functions.<ref name="Meixner"/><ref>[https://genealogy.math.ndsu.nodak.edu/html/id.phtml?id=48491 Meixner] – Mathematics Genealogy Project. Meixner is cited as having been the Ph.D. thesis advisor for students in 1962, 1964, and 1967, at the Rheinisch-Westfälische Technische Hochschule Aachen.</ref>

==Selected Literature== *{{cite journal|last=Meixner|first=J.|year=1933|title=Die Greensche Funktion des wellenmechanischen Keplerproblems|journal=Mathematische Zeitschrift|volume=36|issue=1|pages=677–707|doi=10.1007/BF01188644|s2cid=121262754 }}. This is Meixner's doctoral thesis at Munich, submitted for publication 14 July 1931. *{{cite journal|last=Meixner|first=J.|year=1954|title=On the Thermodynamic Theory of the Second Viscosity|journal=Proceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences|volume=226|issue=1164|pages=51–56|doi=10.1098/rspa.1954.0234|bibcode = 1954RSPSA.226...51M |s2cid=120511525 }} *{{cite journal|last=Meixner|first=J.|year=1973|title=The entropy problem in thermodynamics of processes|journal=Rheologica Acta|volume=12|issue=3|pages=465–467|doi=10.1007/BF01503000|bibcode=1973AcRhe..12..465M |s2cid=95098328 }}. Meixner is cited as being at the ''Institut für theoretische Physik, RWTH Aachen''. Received: 27 October 1972. *{{cite journal|last=Meixner|first=J.|year=1982|title=Constitutive equations of the differential type as approximations|journal=Rheologica Acta|volume=21|issue=4–5|pages=398–399|doi=10.1007/BF01534300|bibcode=1982AcRhe..21..398M }}. Meixner is cited as being at the ''Institut für Theoretische Physik, Rhein.-Westf. Technische Hochschule'' Aachen, Germany. Received: 19 May 1982.

==Books== * J. Meixner and F. W. Schäfke ''Mathieusche Funktionen und Sphäroidfunktionen'' (Springer-Verlag, 1954) ** J. Meixner, F. W. Schäfke, and G. Wolf ''Mathieu functions and spheroidal functions and their mathematical foundations: further studies'' (Springer-Verlag, 1980) * J. Meixner, editor ''Statistical Mechanics of Equilibrium and Non-equilibrium'' Proceedings of the International Symposium on Statistical Mechanics and Thermodynamics held June 15–20, 1964, in Aachen, Germany. (North-Holland Publishing Co., 1965)

==Edited books== * Sommerfeld, Arnold ''Vorlesungen über theoretische Physik. Band 5: Thermodynamik und Statistik. Herausgegeben von Fritz Bopp und Josef Meixner.'' (Diederich, 1952) * Sommerfeld, Arnold ''Vorlesungen über theoretische Physik. Band 2: Optik. 2. Auflage, bearbeitet und ergänzt von Fritz Bopp und Josef Meixner.'' (Akademische Verlagsgesellschaft, 1959) * Sommerfeld, Arnold ''Vorlesungen über theoretische Physik. Band 3: Elektrodynamik. 3. Auflage, bearbeitet und ergänzt von Fritz Bopp und Josef Meixner.'' (Akademische Verlagsgesellschaft, 1961)

==Notes== {{Reflist}}

==External links== *[https://mathworld.wolfram.com/Meixner-PollaczekPolynomial.html Meixner-Pollaczek Polynomials] – Wolfram MathWorld *[https://mathworld.wolfram.com/Meixner-PollaczekPolynomial.html Meixner Polynomials 1st Kind] – Wolfram MathWorld *[https://mathworld.wolfram.com/MeixnerPolynomialoftheSecondKind.html Meixner Polynomials 2nd Kind] – Wolfram MathWorld

{{DEFAULTSORT:Meixner, Josef}} Category:1908 births Category:1976 deaths Category:20th-century German physicists Category:Rheologists Category:Fellows of the American Physical Society Category:LMU Munich alumni Category:Academic staff of the University of Giessen Category:Academic staff of the Humboldt University of Berlin Category:Academic staff of RWTH Aachen University Category:People from Starnberg (district) Category:Scientists from Bavaria