June issue of AJPJune 2020 Issue,

Volume 88, No. 6


Schrödinger's original struggles with a complex wave functionSchrödinger's original struggles with a complex wave function

In this paper, some of Schrödinger's initial struggles with the complex nature of his wave function are outlined. It is shown that he first attached physical meaning only to its real component and even tried to avoid the explicit appearance of the imaginary unit i in his fundamental (time-dependent) equation. This attitude is quite understandable, since he was committed to the classical framework of wave theory, not only ontologically, but also formally. Around one year after the publication of his famous papers on wave mechanics, Schrödinger seems to have accepted that the wave function must be complex and that the physical interpretation is to be related to its absolute square. This is justified by him both due to equivalence considerations with matrix mechanics and in analogy with Maxwell's equations. It is argued that an awareness of the struggles Schrödinger went through to accept a complex wave function can be a relief to students who themselves wonder why ψ needs to be complex when they encounter the topic for the first time.

What is unpleasant here, and indeed directly to be objected to, is the use of complex numbers.
ψ is surely fundamentally a real function (Schrödinger to Lorentz on June 6, 1926, our emphasis).1


Editorial: Blurbs, round II by Richard Price. DOI: 10.1119/10.0001228


Incorrect predictions made by a popular flat-earth model by Bruce Sherwood. DOI: 10.1119/10.0000269


Quantum mechanics in power-law potentials by Sanjoy Mahajan. DOI: 10.1119/10.0001197


Schrödinger's original struggles with a complex wave function by Ricardo Karam. DOI: 10.1119/10.0000852

The Péclet number of a casino: Diffusion and convection in a gambling context by Cedric J. Gommes and Joe Tharakan. DOI: 10.1119/10.0000957

Magnetostriction measurements with a low-cost magnetostrictive cantilever beam by D. Laumann, P. Hayes, C. Enzingmüller, I. Parchmann and E. Quandt. DOI: 10.1119/10.0000640

Experiment on percolation for Introductory Physics Laboratories—A case study by Daniel Dziob and Dagmara Sokolowska. DOI: 10.1119/10.0000810

Rolling along a square path: The dynamics of biased balls by Michael S. Wheatland, Rodney C. Cross, Andrew Ly, Michael Sacks and Karl Smith. DOI: 10.1119/10.0000905

Form of spinning liquids in diverse geometries by Paul Menker and Andrzej Herczynski. DOI: 10.1119/10.0001178

Computer simulation of Mermin's quantum device by Robert Ross. DOI: /10.1119/10.0000833


A fully manipulable damped driven harmonic oscillator using optical levitation by Javier Tello Marmolejo, Oscar Isaksson, Remigio Cabrera-Trujillo, Niels C. Giesselmann and Dag Hanstorp. DOI: 10.1119/10.0000960


A note on a straight gravity tunnel through a rotating body by Aleksander Simonic. DOI: 10.1119/10.0001181


The Hellmann–Feynman theorem at finite temperature by Marina Pons, Bruno Juliá-Díaz, Artur Polls, Arnau Rios and Isaac Vidaña. DOI: 10.1119/10.0001233


Falling Felines and Fundamental Physics by David L. Hu. DOI: 10.1119/10.0001095


American Journal of Physics 88, 512 (2020); https://doi.org/10.1119/10.0001188

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