Schrödinger’s Struggles with a Complex Wave Function

Ricardo Avelar Sotomaior Karam

Abstract

In this contribution I outline some of Schrödinger’s initial resistance to the complex nature of his wave function. It is shown how he first attached physical meaning only to its real component and even tried to avoid the explicit appearance of the imaginary unit in his fundamental (timedependent) equation. This attitude is quite understandable, since he was committed to the classical framework of wave theory, not only ontologically, but also formally. Around two years 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. This episode can be of special pedagogical relevance as students often struggle with the complex nature of the wave function on their first encounter with it.

Original language	English
Publication date	2019
Publication status	Published - 2019
Event	History for Physics: Quantum Foundations - Institute for Quantum Optics and Quantum Information, Vienna, Austria Duration: 23 Sept 2019 → 24 Sept 2019 https://www.mpiwg-berlin.mpg.de/page/history-physics

Conference

Conference	History for Physics
Location	Institute for Quantum Optics and Quantum Information
Country/Territory	Austria
City	Vienna
Period	23/09/2019 → 24/09/2019
Internet address	https://www.mpiwg-berlin.mpg.de/page/history-physics

Cite this

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title = "Schr{\"o}dinger{\textquoteright}s Struggles with a Complex Wave Function",

abstract = "In this contribution I outline some of Schr{\"o}dinger{\textquoteright}s initial resistance to the complex nature of his wave function. It is shown how he first attached physical meaning only to its real component and even tried to avoid the explicit appearance of the imaginary unit in his fundamental (timedependent) equation. This attitude is quite understandable, since he was committed to the classical framework of wave theory, not only ontologically, but also formally. Around two years after the publication of his famous papers on wave mechanics, Schr{\"o}dinger 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{\textquoteright}s equations. This episode can be of special pedagogical relevance as students often struggle with the complex nature of the wave function on their first encounter with it.",

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N2 - In this contribution I outline some of Schrödinger’s initial resistance to the complex nature of his wave function. It is shown how he first attached physical meaning only to its real component and even tried to avoid the explicit appearance of the imaginary unit in his fundamental (timedependent) equation. This attitude is quite understandable, since he was committed to the classical framework of wave theory, not only ontologically, but also formally. Around two years 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. This episode can be of special pedagogical relevance as students often struggle with the complex nature of the wave function on their first encounter with it.

AB - In this contribution I outline some of Schrödinger’s initial resistance to the complex nature of his wave function. It is shown how he first attached physical meaning only to its real component and even tried to avoid the explicit appearance of the imaginary unit in his fundamental (timedependent) equation. This attitude is quite understandable, since he was committed to the classical framework of wave theory, not only ontologically, but also formally. Around two years 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. This episode can be of special pedagogical relevance as students often struggle with the complex nature of the wave function on their first encounter with it.

M3 - Conference abstract for conference

T2 - History for Physics

Y2 - 23 September 2019 through 24 September 2019

ER -

Schrödinger’s Struggles with a Complex Wave Function

Abstract

Conference

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