Heisenberg’s quantum mechanics and the wave-particle duality

by Prof. Sándor Varró (ELI-ALPS Research Institute, Szeged, Hungary)

Friday 12 Sept 2025, 14:00 → 15:00 Europe/Budapest

Tanácsterem (III. ép.)

Hundred years ago Werner Heisenberg published the very first paper of modern quantum theory [1], formulating the basics of matrix mechanics [2a-b]. Based on the reminiscences of Heisenberg, we attempt to keep track of the development of the theory around the time of this discovery. Then we deal with the Heisenberg uncertainty relation [3a], which came out from an analysis of physical observations, by using Born’s probability interpretation [3b]. The so-called Drei Männer Arbeit (three men’s work) of Born, Heisenberg and Jordan [2b], submitted in the year 1925, will also be highlighted. This work also contains a first version of field quantization; the quantization of the normal modes of an oscillating string. The authors derived an analogue of Einstein’s fluctuation formula (1909), for expressing the wave-particle duality of black-body radiation [4]. This is the basis of various correlation phenomena, like e.g. the Hanbury-Brown and Twiss effect. Finally, the field-like description of quantum phenomena, invented by Kornél Lánczos [5a] and Erwin Schrödinger [5b], and the question of equivalence with the matrix mechanics will also be discussed.

[1] Heisenberg W, Über quantentheoretische Umdeutung kinematischer und mechanischer Beziehungen. Zeitschrift für Physik 33 , 879-892 (1925).

[2a] Born M, Jordan P, Zur Quantenmechanik. ZS. f. Phys. 34, 858-888 (1925). [2b] Born M, Heisenberg W, Jordan P, Zur Quantenmechanik. II. ZS. f. Phys. 35, 557-615 (1926).

[3a] Heisenberg W, Über den anschaulichen Inhalt der quantentheoretischen Kinematik und Mechanik. Zeitschrift für Physik 43, 172-198 (1927).

[3b] Born M, Quantenmechanik der Stoßvorgänge. ZS. f. Phys. 38, 803-827 (1926).

[4] Varró S, Einstein’s fluctuation formula. A historical overview. Fluctuation and Noise Letters 6, R11-R46 (2006). [ E-print: http:// arxiv.org : quant-ph/0611023 ].

[5a] Lánczos K, Über eine feldmäßige Darstellung der neuen Quantenmechanik. ZS. f. Phys 35, 812-830 (1926).

[5b] Schrödinger E, Quantisierung als Eigenwertproblem. Ann. der Phys. 79, 361-376 (1926).