ELFT HÍRADÓ

[Zimányiné Horváth Vera <Vera.Horvath AT eli-alps.hu>]

Előadó:              Varró Sándor

Cím:                 Quantum mechanics and signal processing

Időpont:              2026. március 27.,  9 óra
Helyszín:            az ELI ALPS konferenciaterme (Szeged, Wolfgang Sandner 
utca 3.)

Absztrakt:
It has more than a symbolic significance that Max Born, one of the founders 
of quantum mechanics, and Norbert Wiener, one of the main personalities in 
the science of signal analysis and stochastic processes, published a joint 
paper just 100 years ago [1], in which they proposed a new formulation of 
quantum laws. Though this approach was motivated by the eariler, merely 
formal operator calculus, it anyway nicely indicates the overlap of the 
mathematical tools of quantum mechanics and signal analysis. The present talk 
is devoted to discuss this connection in a broader scope, concerning the 
following subjects:
Schmidt decomposition [2] and entanglement;
Riesz-Fischer theorem [3] and equivalence of wave mechanics and matrix 
mechanics;
Haar’s system of orthogonal functions [4], Haar measure [7], frames and 
wavelet analysis;
Plancherel’s Fourier reconstruction theorem [5] and Wigner functions;
Neumann lattice in quantum mechanics [6] and the Gábor information cells [8];
Gábor’s theory of communication [9] and electron-photon entanglement.
The relevance of the above subjects in nowadays research will be illustrated 
on the basis of our recent results in strong field physics and quantum optics.

[1] Born M und Wiener N, Eine neue Formulierung der Quantengesetze für 
periodische und nicht periodische Vorgänge. Zeitschrift für Physik 36, 
174-187 (1926).
[2] Schmidt E, Entwicklung willkürliche Funktionen nach Systemen 
vorgeschriebener. Diss. Göttingen 1905. Mathematische Annalen 63, 433-476 
(1907).
[3] Riesz F, Sur les systèmes orthogonaux de fonctions. Comptes rendus, 18 
mars, 615-619 (1907). Fischer E, Sur la convergence en moyenne. Comptes 
rendus, 13 mai, 1022-1024 (1907).
[4] Haar A, Zur Theorie der orthogonalen Funktionensysteme. Diss. Göttingen 
1909. Mathematische Annalen 69, 331-371 (1910).
[5] Plancherel M, Contribution à l’étude de la représentation d’une fonction 
arbitraire par des intégrales défines. Rendiconti del Circolo Matematico di 
Palermo 30, 289-335 (1910).
[6] Neumann J v 1931 Die Eindeutigkeit der Schrödingeschen Operatoren. 
Mathematische Annalen 104, 415-458 (1931).
[7] Haar A, Der Maßbegriff in der Theorie der Kontinuierlichen Gruppen.  
Annals of Mathematics 34, 147-169 (1933)
[8] Gabor D, Theory of communication. The Journal of the Institution of 
Electrical Engineers 93, Part III, 429-457 (1946).
[9] Gabor D, Communication theory and physics. Philosophical Magazine Ser. 7, 
41 (322), 1161-1187 (1950).

A szeminárium angol nyelvű. Minden érdeklődőt szívesen látunk. A szeminárium 
online is meghallgatható:

https://teams.microsoft.com/l/meetup-join/19%3ameeting_OWY1Y2Y0MmMtODNjYS00ZmUwLWJkNWQtNzU0N2Q0MTBhYjhk%40thread.v2/0?context=%7b%22Tid%22%3a%22b207389a-c5cb-4cb0-a1ad-227b94e96448%22%2c%22Oid%22%3a%22c993efcb-59ae-4652-9f68-d7a313727128%22%7d

Üdvözlettel:

ZIMÁNYINÉ HORVÁTH Vera
Látogatóközpont-vezető

TEL             +36 70 491 1412
EMAIL     vera.horvath AT eli-alps.hu<mailto:vera.horvath AT eli-alps.hu>
WEB         www.eli-laser.eu<http://www.eli-laser.eu> | 
www.eli-alps.hu<http://www.eli-alps.hu>
[A black and orange logo  AI-generated content may be incorrect.]
The Extreme Light Infrastructure ERIC | ELI ALPS Facility
Wolfgang Sandner utca 3., H-6728 Szeged, Hungary