ELFT HÍRADÓ

[mcsete AT physx.u-szeged.hu]

Seminar

Speaker: Professor Sándor Varró
ELI-ALPS (Attosecond Light Pulse Source) Research Institute, Szeged, Hungary.

Date: 3 pm, 19, March (Wednesday) 2025
Location: University of Szeged, Institute of Physics, Zoltán Bay class-room
& online https://join.skype.com/tIRReLaRNWY7

Title:
On Heisenberg’s quantum mechanical reinterpretation
of kinematic relations and the wave-particle duality.

Abstract:
Hundred years ago Werner Heisenberg published the very first paper of  
modern quantum theory [1], formulating the basics of “matrix  
mechanics” [2]. In the present talk we attempt to follow the  
development of quantum theory around the time of this discovery. First  
we illustrate that in quantum mechanics even the kinematics of the  
motion of a microparticle is reinterpreted, so that its position and  
momentum are described by non-commuting matrices. This is in sharp  
contrast to our picture of the classical motion of a particle, which  
takes place along some trajectory. We shall also highlight the “Drei  
Männer Arbeit” (three men’s work) of Born, Heisenberg and Jordan [2],  
submitted also in the year 1925. This work - besides giving solutions  
to several fundamental problems constituting today basic parts of any  
standard texts on quantum mechanics - contains a first version of  
field quantization, namely, the quantization of the normal modes of an  
oscillating string. As an application of this new formalism, the  
authors derived [2] an analogue of Einstein’s fluctuation formula  
(1909) expressing the “wave-particle duality” of black-body radiation  
[5]. According to this result, both the wave-like and the  
particle-like fluctuations are simultaneously showing up, which is  
characteristic e.g. in the Hanbury Brown and Twiss type intensity  
correlations, or in the fluctuation of the number of particles in a  
gas satisfying the Bose-Einstein statistics (1924). We shall also deal  
with Heisenberg’s “uncertainty relation” [3] coming from an analysis  
of physical observations, by using Born’s probability interpretation  
[2a]. Finally, we present a brief comparison of wave mechanics and  
matrix mechanics with the help of two examples: the harmonic  
oscillator coherent wave packets derived by Schrödinger [4], and the  
squeezed state amplitudes constructed by Kennard [3a], who used the  
transformation theory of Jordan [3b] and Dirac [3c].

[1] Heisenberg W, Über quantentheoretische Umdeutung kinematischer und  
mechanischer Beziehungen. Zeitschr. für Physik 33 , 879-892 (1925).
[2] Born M, Heisenberg W und Jordan P, Zur Quantenmechanik. II.  
Zeitschr. für Physik 35, 557-615 (1926). [2a] Born M, Zur  
Quantenmechanik der Stossvorgaenge. Ibid. 38, 803-827 (1926).
[3] Heisenberg W, Über den anschaulichen Inhalt der  
quantentheoretischen Kinematik und Mechanik. Zeitschr. für Physik 43,  
172-198 (1927). [3a] Kennard E H, Ibid. 44, 326-352 (1927). [3b]  
Jordan P, Ibid. 40, 809-838 (1927). [3c] Dirac P A M, Proc. Roy. Soc.  
A 113, 621-641 (1927).
[4] Schrödinger E, Der stetige Übergang von der Mikro- zur  
Makromechanik. Die Naturwissenschaften 14, 664-666 (1926).
[5] 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 ].


Everyone is welcome to attend.

Dr. Mária Csete

----------------------------------------------------------------
This message was sent using IMP, the Internet Messaging Program.

Attachment: png07XfNJgIpr.png
Description: PNG image

Attachment: Varro_S_Heisenberg_SZTE_19_March_2025.pdf
Description: Adobe PDF document